Greetings, and welcome to my guide.
I liked Room 2 a lot more than Room 1 - i thought the puzzles were more fair/reasonable, so I wanted to provide some little hints in case you get stuck so you can enjoy solving it yourself as well.

To further this I've also hidden the order in which the puzzles must be solved.

1. The White Room
   
2. The Cube Safe
   
3. The Science Room
   
4. The Grey World
   
5. The Fountain
   
6. The Force Field Gate
   
7. Bonus (for and Achievement)
   
8. Speedrun

Description: After starting the level, you'll find yourself in a mostly-white void

Hints:

1. Look around - other than the lobby do you see anything?
   
2. That door looks a bit messed up, doesn't it?
   
3. I didn't get a hotspot, but some of the door fragments can be clicked on
   
4. Solution: Various door fragments will rotate when clicked - keep clicking on them until they rotate into the correct position. There is a small triangle in the topish right that can get covered by larger pieces; you may wish to do that one first. Once complete, the door will open, allowing you to descend the floating rocks until you're able to jump down to the grass below

Red Herring: The puff of smoke when you click on a mask reveals the world outside the white chamber - rapid clicking can reveal a lot of the world. As far as I can tell, this is just a result of how the special effects work and has no meaning or purpose.

How to find the next puzzle?
Once you are down, you will see a large room with a glass wall - on the wall is a note that's mostly scribbled out, but at least the first object is visible. Is there something like that around you?

Description: Between the large glass-fronted room and the blue force-field gate is a large stone arch leading to a small clearing. In the clearing is a keypad locked cabinet with an arrangement of orange and purple cubes

Hints:

1. Hildebrand starts you off - there are a lot of little cubes missing from this big cube.
   
2. The keypad takes a 2-digit number
   
3. You need to figure out how many little cubes are missing
   
4. How big is the cube supposed to be?
   
5. The longest intact side is 6... that means it should be (at least) a 6x6x6 cube
   
6. That also means the entire top layer is missing - that's 6x6 or 36 cubes to start - now count the rest of the missing ones...
   
7. Solution: Enter 65 into the keypad and hit the arrow

Red Herring
The initial note shows the cube as a 3x3x3; it's just there to convey the idea of "cube".
As far as I can tell, that "42" has no meaning; but we'll revisit for the last puzzle.

How to find the next puzzle?
Grab the handle from the cabinet and return to the main area and have a look around.
What has changed?

The glass wall blocking the large room has vanished, maybe you can go there?

Description: After you open the Cube cabinet and get the handle, the glass wall blocking the large room disappears allowing you to enter and investigate.

Interface Defects!
This puzzle requires you to place a number of objects on hotspots, but attempts can fail for a number of reasons. If you keep clicking and nothing happens, I've found three things that seem to make a difference. First, the game seems to want you to actually pick up and maybe examine the "correct" painting with the solution. Second, the game seems to want you to actually examine and rotate the object so you can "see" the symbol. Third, if there is another object floating in space too close to the hotspot, the game won't let you place the correct object, so you may need to clear the area a little.

Hints:

1. First, where can you use that handle? Does anything look mechanical?
   
2. On the left side of the room is a round table with tripod wheels - it'll take the handle
   
3. Now that your hands are free, have a look around - there are three things of interest here:
   
   1. Child-like paintings with basic shapes
      
   2. A number of objects you can pick up
      
   3. A number of flat surfaces that reveal a white shape outline when you hover the mouse over them
   
   
4. Is there anything similar between the child-like paintings and the shape outlines?
   
5. The painting leaning on the desk has a pentagon - did you find a pentatgon?
   
6. So it can't be the one with the pentagon, what about the other two?
   
7. What if it's a top-down view?
   
8. The one by the casket with the green triangle, yellow circle, and red square has the shapes in the wrong order compared to the room, so it can't be that one either
   
9. Therefore it has to be the one by the girl with the red triangle, green square, and yellow circle. I think you have to actually pick this object up before the game will allow you to place the objects later. You might want to put it on the ground aligned with the shapes, but you don't need to
   
10. Now that you have a key for the various shape colours, where will you get colour?
    
11. Did you try rotating any of those other objects you can pick up?
    
12. Oh that's neat, they have little colourful shapes on the bottoms!
    
13. Can you find objects that match the shape and colour from your painting?
    
14. Yellow Circle - there is a sculpted head of Morpheus on top of the locked glass cabinet - take it down, see the yellow circle, and then left-click on the circle outline on the left side of the table with the mirror
    
15. Red Triangle - on the table under the mirror, there is a red book with lots of gold leaf you can pick up on the top of the stack of books on the right side. Take it, turn it to see the red triangle, then left-click on the triangle outline on the circular table where you used the handle.
    
16. Green Square - on top of the hutch on top of the desk there is a small "bottle of chemicals". Pick it up and rotate it to see the green square - then left-click it on the white square outline on the desk
    
17. You put the three objects down... so why did nothing happen?
    
18. Didn't you put a handle on the circular table? Surely it's there for a reason...
    
19. The circle-table has a triangle right? How is it rotated compared to the painting?
    
20. Rotating the table will also rotate the triangle...
    
21. If you rotate the table so the triangle is on the side facing the two adults, it'll be in the same orientation as it is in the painting. You may need to pick up and replace the book, but I didn't.
    
22. When you have everything correct, Hildebrand will notice and the glass cabinet will open - go to it and take the odd metal rod with the ball.

Where to go next?

1. Now that you have the brass rod-thing from the glass cabinet, so you see any other large brass things?
   
2. If you back out of the large room and move counter-clockwise through the clearing, there is a large brass rod that starts the 4th puzzle...

Description: You've solved the cube cabinet to gain access to the large room, and now you have the brass rod

Interface Defect:

1. After placing the rod, you will be told that the device is active, but you need to click on it another time for it to matter. Not a defect per se, but I was stuck on it for a while >_<
   
2. The masks have to be put in place after you activate the device and shift to the grey world. If you place the masks while you're still in the colour-world, you may need to pick one up and put it back for the even to trigger.

Hints:

1. If you look at the large brass thing in the main clearing - it's a bit like a Van Der Graf generator - the game will tell you something is missing.
   
2. The brass rod you got from the glass cabinet in the large room is a something
   
3. Using the brass rod on the large brass thing and the game will tell you the machine works now... does that seem a little specific?
   
4. Click the machine again to activate the machine - this will move you from "the colour world" to the "grey world" - you'll also know it worked because in the grey world only there is a charter of letters (N through V) on the large brass thing. Note: you can keep clicking on the machine to move between worlds if you want to.
   
5. At the base of the machine you may have noticed something?
   
6. There are four bunny masks at the base of the machine. Have you seen bunnies elsewhere? Note: the bunny mask you can choose as a player doesn't count and isn't part of this puzzle.
   
7. Wasn't there a piece of paper in the glass cabinet in the large room where you go the brass rod?
   
8. Have you noticed the grey rocks around the clearing? If you have trouble finding them (because everything is grey now) you can shift back to the colour world by clicking the brass machine.
   
9. Each of those rocks has a little bunny logo on it... what could that mean?
   
10. If you pick up a mask an use it on a rock, but how do you choose which rocks to give masks to? There are seven rocks in total, and four masks...
    
11. There are two ways to solve this...
    
12. The visual way (wrong, but it works) If you just place a mask on the rock right by the brass machine, you'll see it faces in a direction...
    
13. Assuming that's a hint, why would it do that and why would there be more than one mask?
    
14. One mask gives you a line, right? How can you narrow that down?
    
15. There's another rock to the left of the path to the fountain, why not try a mask there?
    
16. The mask there looks in a line that crosses the sight of the first mask...
    
17. So if all the masks' lines of sight are supposed to cross, you can eliminate the two in the small clearings (one with the fountain and the one with the cube cabinet)... that just leaves three rocks for two masks...
    
18. There's a rock just to the right of the large room, that has a nice view of the big clearing...
    
19. That leaves two more rocks - one next to the huge tree and one half-way between the huge tree and the blue forcefield
    
20. You want the one between the huge tree and forcefield.
    
21. The clue way (correct, but maybe harder) In the glass cabinet with the brass rod, there was also a piece of paper labelled "you and your friends reunited under the black veil".
    
22. That paper is a map... but how do you orient it?
    
23. The X's are obvious - four X's for four masks, but that's that circle with the bear head?
    
24. Have you looked at the fountain?
    
25. The large spouts on the fountain are bear heads - that means the circle must be the fountain! - Actually, on my third playthrough I realized the rock in the fountain clearing has an icon of a bear on it in the grey world. Oops!
    
26. Now that you can orient the map
    
27. Okay so four X's, and there are four bunny masks at the brass machine...
    
28. There is really only two possible solutions because there are only 5 bunny rocks in the main clearing, and only two are close together.
    
29. One goes right by the brass machine, one goes just left of the entrance to the bear fountain, one to the right of the large room. There are two between the huge tree and the blue forcefield - you want the one in the middle, not the one next to the tree.
    
30. Simple Solution (thanks to OrangeDog):When in the grey world, a second symbol appears on every bunny rock. The correct rocks are: Angler-fish (by the brass machine), Eel (by the entrance to the fountain clearing), Prawn (by the large room) and Octopus (between the huge tree and blue forcefield).
    
31. After the puzzle:You'll know the game accepted your solution when the game talks to you - if it doesn't make sure you're in the grey world and try picking up and replacing masks - it seems to only "count" if finish it in the grey world.
    
32. Aside from the obvious, what else has changed?
    
33. Where all the masks align, you'll see a crackling (but silent) energy ball - take it

Red Herrings
The letter chart is technically a clue for the next puzzle, ignore it.
The bunny rocks in the small clearings are just noise; ignore them.

Where to go next?
Once you have the energy ball, look around, are there more energy balls elsewhere?

Description: Now that you have gotten past the cube cabinet, the large room, and gotten the energy ball from the grey world, it's time to make use of your new object.

The Letter Code
I'm bring this to your attention because there is a sub-puzzle in this stage that, as far as I can tell is never explained in-game, and without knowledge of Greek Myth, will just be a very distracting Red Herring.

1. There is a note at the base of the fountain - at the top right, there are some white symbols
   
2. This is an old children's code called "Pigpen" for reasons that will become clear
   
3. Scattered through the level are four decoder sheets - you only need three to get the answer (or none, if you happen to know Pigpen)
   
4. J-M is on the fountain rim, just right/counter-clockwise of Hildebrand's note
   
5. W-Z is hidden in the boughs of the pine tree immediately to the right of the entrance to the bear fountain when you're looking in
   
6. N-V is attached to the brass machine, but only in the grey world.
   
7. A-I is against the huge tree immediately right/counter-clockwise from the clock
   
8. How the code works: The decoder sheets have a "pig pen" drawn and an arrangement of letters. The code for each letter is the lines (with or without a dot) corresponding to the cell in the position of the letter. So of you look at the J-M sheet, all without dots, J is \/, K is <, L is /\, and M is >
   
9. Using these, you should be able to translate the symbols - give it a try, you're bound to find this code in other games later
   
10. What is says: Putting together the letters, you'll get the word LETHE, which doesn't appear to be explained or directly used anywhere in the level.
    
11. Why it matters: In Greek mythology, the River Styx transports the dead to the underworld. The River Lethe washes away their memories. Throughout this level, there are numerous references to memories, difficulty remembering, etc. In particular, you will notice that the now-overflowing fountain is also labelled with "LETHE" in code - this is how you know you're supposed to stop the fountain rather than turning on all the spouts. Maybe coincidence, maybe not - some Greek sects also believed that drinking the waters of the Lethe and forgetting your past life allowed souls to reincarnate.

Hints:

1. Now that you have the energy orb, what should you do with it?
   
2. Where else do you see similar orbs?
   
3. To the left of the large room is a small clearing with a fountain (that is currently flooding the level) - bring the orb there and click on the fountain
   
4. You may notice glowing symbols on the fountain as well as on the note - you can solve them in "the Letter Code" I've outline above, but they're really a distraction.
   
5. Around the fountain are six energy orbs - each with a Greek letter and a number value
   
6. As far as I can tell, the letter and the number mean nothing - however, try clicking on some orbs and see what happens...
   
7. Each orb turns a set of spouts on or off, that's neat...
   
8. If you haven't touched the fountain you will have seen all six spouts active, so that can't be the solution. Also, if you know your Greeks and solve the Letter Code, you can get a good hint, but you probably don't need it.
   
9. If all the spouts is wrong, why not try none of the spouts?
   
10. But why? From the Letter Code, the fountain is labelled "LETHE", which is the river that erases memories. The implication is that this overflowing fountain is the source of all the memory problems, and therefore you can fix them by stopping the fountain. That's also not how the Lethe works in mythology - the gods themselves couldn't undo its effects, but no matter.
    
11. If you poke at it a bit, you should be able to figure it out, the relationships are simple.
    
12. • Alpha-12 turns on Alpha and turns off Psi
      
    • Beta-5 turns off Lambda and Mu (= good)
      
    • Delta-19 turns on Alpha, Beta, and Delta (= bad)
      
    • Lambda-20 turns off Beta and turns Lambda on
      
    • Mu-8 turns off Delta and Alpha (= good) and turns on Mu
      
    • Psi-4 turns on Lambda, Mu, and Psi (= bad)
    
    
13. So, Lambda turns off Beta, Alpha turns off Psi, Mu handles Alpha, Delta, and finally Beta turns of Lambda and Mu - transliterated to English, that does spell "Lamb" (e.g. sacrifice?), but I think that's coincidence. Google translate tells me it's also Greek for "received", but that seems coincidental as well.
    
14. You'll know you've done it when Hildebrand tells you to get the final number and leave.

Where to go next?
There are really only two questions left - what number? And where to leave?

Description: Having solved all the other puzzles, Hildebrand has told you to gather the numbers and leave.

Hints:
Where? At this point, there should only be one place left to go - to the right of the blue forcefield blocking the smaller arch is a keypad that takes a 6-digit number. Enter the code and you're done.

What?

1. The very first note against the glass wall of the large room noted that the puzzles were in a specific order
   
2. You may have noticed that each of the puzzles had numbers attached - 42 for the cube cabinet, 99 in the glass cabinet in the large room, 59 on the fountain, if you happen to visit it after you solve the puzzle in the colour world.
   
3. Entering 429959 doesn't work?!
   
4. You didn't solve the last puzzle in colour space, did you? (no you didn't)
   
5. If you go to those sites in grey space, they have different numbers!
   
6. 29 in the cube cabinet, 11 in the large room glass cabinet, 87 on the fountain. Possibly a birthday - 29 November 1987
   
7. Solution: Enter 291187 into the keypad

Unsolved Mystery:
I have no idea what significance, if any, the colour world code - 429959 has. My best guess is that it's to show a vague memory of there being a code, but no memory about what the code was.

After you beat the room:

1. Hit close to continue playing - you can now explore past the forcefield
   
2. Is any object out of place?
   
3. There's an odd spikey dish-thing on the left...
   
4. Do you remember anything else out of place?
   
5. There's a wooden UFO toy in the large room - it should be near the left side of the desk
   
6. Bring the UFO to the spikey dish-thing.

1. Start a new game in Room 2
   
2. Open the door to the lobby
   
3. Hold Space to skip the cinematic
   
4. You only need to follow the stairs for the first maybe quarter turn - then you can fall off the side
   
5. Run straight to the blue forcefield and enter 291187 into the keypad
   
6. The game will not like this and it will seem like it's broken, especially if you use space to skip the next cinematic
   
7. After was feels like forever (so maybe 5 seconds) the forcefield will disappear and you can enter the last chamber to stop the clock. If for some reason it doesn't try opening the cube cabinet (code = 65)