Steam – Remote download on free games

Yes, games linked to your Steam account can be installed / uninstalled at will.

There are some rare exceptions where a game has additional DRM that limits the number of times you can install - but this should always be noted on the game's store page (the first example I've found is Dead Space 2, check the wall of capitalised text carefully to see what I mean) and there is often a way to "reclaim" those installs before you uninstall the game. So check the Store page for each game before you uninstall if this is a concern.

When you want to reinstall:
On your game list, if you switch to the "All Games" view you will find all the games you have linked to your account. Those that are not currently installed will be greyed out, and from here you can select for them to be downloaded and installed.

Pretty much. Or more precisely, if you try to start it after the free period passes, steam will attempt to authenticate that you own the game, realize that you don't, and refuse to start the game.

I don't think it deletes the data, mind - after all, it's in their best interest to make it as easy as possible for you to decide to buy the game - but until and unless you actually buy the game it's just taking up several gigabytes of space on your hard drive.