In a multiplayer game, once an opponent leaves the game, they won't be considered for such an effect, no matter how many cards they had in their graveyard before leaving the game.

If a creature on the battlefield has {X} in its mana cost, X is considered to be 0.

Once Lullmage's Domination resolves, the control effect lasts until the creature leaves the battlefield or you lose the game. It doesn't expire at the end of turn.

An ability that offers a bonus if an opponent has eight or more cards in their graveyard won't provide additional benefits if more than one opponent has eight or more cards in their graveyard. There are also no additional benefits no matter how many cards are in an opponent's graveyard, as long as there are at least eight.

To cast Lullmage's Domination, choose a value of X, choose a creature with the appropriate mana value, then determine the spell's cost, subtracting {3} if appropriate. This can't reduce the {U}{U}{U} in the spell's cost. For example, if you wish to target a creature with mana value 2 whose controller has eight cards in their graveyard, you'll pay {U}{U}{U}.