Recently there was a thing where VAC would erroneously flag AMD’s antilag+ feature as cheating, and issue a ban.
AMD then quickly disabled the feature by default but now Valve also patched detection for it and is now, at least according to these patch notes, reversing the bans.
Depends on the game iirc. If you get banned in a Valve game, you don’t get to play multiplayer in any Valve game.
It’s more complicated than that, VAC bans are tied to the version of game engine used. So a VAC ban in Counter Strike Source would have also banned you from TF2, DoDS, and HL2DM, and nothing else. This also means that VAC bans from CSGO don’t affect any other games (except CS2 which is technically the same game)