Normally you only get banned from the game you cheated on. Tbh, nothing you can really do. I mean, I've been VAC banned from MW2 but I could play online again after a while.
you could try contacting valve staff on the forums, other than that nothing you can really do. mw2 used to be a very very glitchy game when it came to false vacs
VAC is permanently ban. They can't remove your ban anytime, or perhaps you cheat. One way to solve the problem, create new steam account and buy other game, it won't detect people's alternate account. I ensure that VAC is only come for the game created by Valve.
VAC can be implemented by any game released on Steam. But typically the ban usually is only for the game you received it on, with some exceptions. A ban on a GoldSouce game is a ban on all GoldSource games, and a ban on a Source game is a ban on all Source games minus CS:GO and Dota 2 (which are treated as separate games).
According to the SteamWorks API documentation, all a game has to do is check if a player is banned, and then the game is secure.
As others suggested, all you can really do is making an alternative account and re-purchase the game. What you then could try is befriending your original account and share the game to your original library after you delete it. Don' think this would work but it's worth a shot.