Steam – Does uninstalling Steam also uninstall games installed through steam

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.

Almost certainly not.

Steam tends to leave at least some things lying around, as it doesn't actually "uninstall", though it obviously depends on the game in question.

Many games also insert their own data into %APPDATA%, %USERPROFILE% or elsewhere, which are unlikely to be removed when you delete the game from Steam.

Edit to add: most of the time, these files will be insignificantly small. But if you want to be super clean, be prepared to look around for the artfacts left behind and don't trust/expect Steam to manage it.