Damage dealt to an opponent causes that player to lose that much life.

Feast on the Fallen looks at the entire previous turn to determine whether its ability triggers or not. It doesn’t matter whether Feast on the Fallen was on the battlefield when the opponent lost life.

Feast on the Fallen checks only if an opponent lost life during the turn, not whether that player’s life total decreased over the course of the turn. For example, if an opponent lost 2 life and then gained 8 life last turn, Feast on the Fallen’s ability will trigger.

Only one +1/+1 counter will be put on the target creature no matter how much life was lost.