Many of them. Pretty much nothing sha based, and nothing Scrypt based, nothing stake based, but most everything else is fine.

Ethereum, Monero, Zcash, Sia off the top of my head, I am pretty confident there are at least a few dozen others as well.

Not feasible if you have to foot the bill. But if you don't...

Check out whattomine or coinwarz for a list.

There are a number of currencies specifically designed to be gpu mineable, in an effort to be more "democratic".