Any abilities that trigger during the resolution of Mass Polymorph (such as a creature's "enters" ability) will wait to be put onto the stack until Mass Polymorph finishes resolving. The player whose turn it is will put all of their triggered abilities on the stack in any order, then each other player in turn order will do the same. (The last ability put on the stack will be the first one that resolves.)

All creatures you put onto the battlefield with Mass Polymorph enter at the same time.

If the number of creatures you exile is greater than the number of creature cards remaining in your library, you'll wind up revealing your entire library, putting all creature cards revealed that way onto the battlefield, then shuffling your library.

The creatures you exile with Mass Polymorph remain exiled for the rest of the game.