If a creature with Persist (and no counters on it) is killed, does it return "immediately" from the graveyard to play or, because it's a triggered ability that goes on the stack, would an opponent have an opportunity to exile it from the graveyard, for example by activating Tormod's Crypt before the triggered ability resolved?
It is a triggered ability and it uses the stack that players can respond to. Almost nothing in the game is "immediate" outside of mana abilities and special actions. Persist is neither which means they can indeed exile your graveyard before the Persist trigger resolves.
When a creature with Persist returns from the graveyard, is it "immediate"?