The amount of life you lose is determined by the mana value of the card in your graveyard, not the creature once it's on the battlefield.

You lose life after the creature is already on the battlefield. Any abilities it has that interact with loss of life, such as that of Platinum Emperion, apply to that loss of life.

In a multiplayer game, if a player leaves the game, all cards that player owns leave as well. If you leave the game, the creature you control from Reanimate is exiled.

If any abilities trigger on the creature entering the battlefield, those abilities resolve after you lose life. If losing life results in you losing the game, those abilities won't resolve.

If a card in a player's graveyard has in its mana cost, X is considered to be 0.