The ammo doesn't absolutely have to be subsonic. It's much quieter if it is but it doesn't have to be.
A suppressor in the USA requires a tax stamp ($200 I think) from the ATF, in addition to the actual purchase price. Might be some local paperwork too.
As for the hunting, I was thinking big game type hunting where I would guess it is mostly illegal, though I'm not sure. For "pest" hunting, unprotected species, invasive species and the like, it's probably legal assuming owning the suppressor is legal in the state.