Steam Library

I believe you can submit a ticket to have specific games removed from your library.

Nope. Only by asking steam support to do this.

Yeah you can, just submit a ticket to Steam Support to remove the game for you.

You can submit a ticket but some betas are tied to the full game and can't be removed. Dunno about TF2, but CS:Source and Red Orchestra 2 are some examples.

You could just view installed games

delete local content will remove it from the list if it's f2p. if you have a premium account i think it hangs around.

it's connected with your account so it wont disappear somehow

Ask steamsupport. They will remove it.

Support can remove game(s) if you ask them to.

The support will remove the games when you ask them, just keep in mind that you won't get it back (even if it's just the TF2 Beta).

Only F2P games are removed when you uninstall them, the Beta counts as a purchased game and you'll need to ask the support.

Team Fortress 2 beta in your library only symbolises the fact that you have Premium, I don't see why it bothers you so much.
However, to answer your question - Yes, you can remove a game, I've done it before with a faulty key which didn't work correctly for some reason.