As Dredge the Mire resolves, first the next opponent in turn order (or, if it’s an opponent’s turn, the opponent whose turn it is) chooses a creature card in their graveyard, then each other opponent in turn order does the same knowing the choices made before them. Then all the chosen cards are returned at the same time.

In a multiplayer game, if a player leaves the game, all cards that player owns leave as well. If you leave the game, any permanents you control from Dredge the Mire are exiled.