If each player has 0 life after Spawn of Mayhem's triggered ability resolves, each player loses the game at the same time and the game ends in a draw.

If Spawn of Mayhem gains lifelink, the damage it deals will cause you to simultaneously lose and gain life. If your life total is 1, you won't lose the game.

In a Two-Headed Giant game, Spawn of Mayhem's last ability causes each team to lose 2 life. Then if your team's life total is 10 or less, you put a +1/+1 counter on Spawn of Mayhem.

Spectacle doesn't change when you can cast the spell. For example, you can't cast a sorcery with spectacle during an opponent's turn unless another effect allows you to do so, even if that player has lost life this turn.

Damage dealt to a player causes that player to lose that much life.

In a multiplayer game, if an opponent loses life and later that turn leaves the game, you can cast a spell for its spectacle cost. (If a player leaves the game during their turn, that turn continues without an active player.)

Spectacle cares only that an opponent lost life during the turn, not that the opponent's life total is currently lower than it was. For example, if an opponent loses 1 life and then gains 2 life in the same turn, you can cast a spell for its spectacle cost that turn.

A card's spectacle cost is the same no matter how much life your opponents lost or how many opponents lost life.

To determine the total cost of a spell, start with the mana cost or alternative cost you're paying (such as a spectacle cost), add any cost increases, then apply any cost reductions. The mana value of the spell remains unchanged, no matter what the total cost to cast it was.