Hi ЧPOG, thanks for the detailed feedback! Some of this is quite helpful. I actually just figured out the alt-tabbing issue (Unity wasn't registering the release of the Alt key after alt-tabbing, causing it to lock the player out of any sort of input that required Alt to not be pressed down, most notably camera zoom)--so now I've gotten that fixed for this month's update. 🙂

I agree with you on being able to sort characters on the Army Overview screen--I'll see if I can address these for this month's update. You're also right about certain old equipment from TT being worse than the new TIB variants; that's been on my radar, but going through and tweaking all of the values has just been lower priority than other things on the to-do list so far. I'll get to it eventually!

Regarding some of the other stuff:

2) When you mouse over equipment in the reserve supplies screen, pay attention to which portraits remain lit up and which portraits become grayed out--the portraits which stay lit up are characters who (1) can use the equipment and (2) sense that they can derive some sort of benefit from it (i.e. it's not just a strictly inferior version of something they're already equipped with...unless they're equipped with a weapon that's close to breaking, and then they might want it anyway as a backup weapon). If the item is in a particular character's inventory, meanwhile, it'll be redded out if they can't use it.
3.1) You're supposed to be capped at 18 units, so in theory this shouldn't be necessary. (Have you managed to get beyond 18?)
5) You can do all of this in the Manage Supplies screen. Can you explain what specific changes to it you'd like to see?
7) There is a small delay between turns to allow character animations to finish and to let the in-game camera keep up with what's happening; but If you're seeing any sort of truly meaningful delay, that would likely be because the computer is thinking. (The game currently hard-caps the AI at 2 seconds of thinking between turns, though.)
7.1) This is a Unity issue. Unfortunately, there probably isn't a fix for this short of completely replacing the use of Unity scenes with a hand-rolled solution for loading and unloading assets dynamically along with manual triggering of garbage collection (which would be a ton of work and would likely introduce a variety of bugs, so I'm reluctant to go that route)
10) This is indeed an example of bad luck--but this is also what stat-boosting items and the trainer are for! (Note that training health in particular is quite inexpensive; why not give it a try?)
12) You are correct: learning about your characters by watching and listening to them is a key part of the experience. For this reason, I won't be exposing character backgrounds by default. Most of the backgrounds don't affect stats or skills--but on the occasions where they do, it's mentioned in the tooltip description for them in the custom character creator!
13) Fights start off small to make every nook and cranny in the terrain count--consequently, there's a lot more density here in terms of meaningful terrain variation compared to Telepath Tactics. This is a deliberate design choice. That said, arena fights (and random-event battles) do grow in size as you advance through the game and characters get increased range and mobility, so don't worry: larger-scale fights will arrive if you keep playing!
16) Male and female heroes already do have different sprites! (For species which have sexual dimorphism, anyway--i.e. not shadowlings.) That said, characters of the same class generally have the same uniform/armor in their sprites, so it's often not a super dramatic visual difference--you can see it most easily in classes like axefighters, barudit, photokineticists, and assassins.

I've been able to go over 18 characters for a while now. I have a suggestion for that. Let us set the maximum characters we can have in the custom rules. Like, 9, 18, no limit, or whatever else you want to set up. Of course that would require fixing the issues with having more than 18 characters.

Also, yes, I know how extremely expensive it is to have 18 or more characters, but eh, it's fun to have that many if you can manage the cost (plus Golems help with that since they don't need to be paid and can do labor better than most other classes). Obviously you're never going to have a lot of characters if the base salaries are high (I'd imagine the price would be over 20k per pay period, so... ouch), so this would just be for fun.