If you lose enough life to lower your life total to 0 or less, you’ll lose the game as a state-based actions before you activate Tainted Sigil’s ability.

When Tainted Sigil’s ability resolves, it checks how much life each player lost over the course of the turn, then it totals that number and you gain that much life in one shot. It doesn’t matter how a player lost life or what caused it. It also doesn’t matter if Tainted Sigil wasn’t on the battlefield when some or all of the life was lost.

Tainted Sigil’s ability counts the life lost by all players, including you.

Tainted Sigil’s ability checks only whether life was lost. It doesn’t care whether life was also gained. For example, say one player lost 4 life during the turn and no one else lost any, but that same player also gained 6 life that turn. That player has a higher life total than they started the turn with — but Tainted Sigil’s ability counts only the life loss, so you’ll gain 4 life.