I'm not trying to sell or make a profit or anything. It's just that one of the games I installed I ended up not liking very much. However my friend really wants to give it a try, but I don't know if it'll work since my multiplayer key is used. If I uninstall, will the game 'know' that my key isn't used and thus let my friend use it?
This depends mainly whether the keys used are associated with an account. It used to be that if you gave a friend a game that you no longer wanted and it's key there would not be an issue. Nowadays keys are mainly used in conjunction with some kind of online account making them a one time use deal. So if the game does use an account association for the keys, all you can do is ask to transfer it.