Since the models are intended for TF2 servers, you will need

1. A TF2 server
   
2. Sourcemod
   
3. A plugin which uses playermodels

The most common plugin that uses custom playermodels should be Model Manager, which you can find HERE[forums.alliedmods.net].
(Every model thread has a cfg entry, you can copy and paste into your model manager cfg file)
Of course, you can also use the models for custom bosses, pets, or even projectiles, if you so want.



No!
You can simply put the two folders models and materials into your servers tf root folder and they will be in the right place.
However, if a model has multiple versions, as stated in the thread, you can choose not to put those on your server. The model files will be named appropriately.



Yes you can!

Warning: Most cosmetic items will clip or won't work at all. Also, make sure you are on a server with the right sv_pure settings. Valve servers are not allowing custom content anymore.

You will need to edit some files first. First, create a folder inside your tf/custom folder called "playermodels" (the name doesn't really matter). In this folder create another one called "models" and in this one again a folder named "player". In the end you should have it like this:
tf/custom/playermodels/models/player
Then you put the downloaded files into the folder "playermodels". When done, you copy all the 6 model files of the custom model and paste it into the "player" folder and rename the files accordingly to the playerclass you want to replace. They are

• scout
  
• soldier
  
• pyro
  
• demo
  
• heavy
  
• engineer
  
• medic
  
• sniper
  
• spy

Afterwards, just start the game and you are set.