In multiplayer games, you choose an opponent to separate the cards when the ability resolves. This doesn’t target that opponent. Because the cards are revealed, all players may see the cards and offer opinions.

The creature cards may come from different graveyards.

A pile can have no cards in it. In this case, you’ll choose whether to put all the exiled cards onto the battlefield or into graveyards.

You (not your opponent) choose which pile to put onto the battlefield and which to return to graveyards.

In a multiplayer game, if a player leaves the game, all cards that player owns leave as well. If you leave the game, any creatures you control from Boneyard Parley’s effect are exiled.