Combat damage is the damage that's dealt automatically by attacking and blocking creatures. Any other damage is noncombat damage, even if it's dealt during a combat phase by an attacking or blocking creature.

The last ability of Wildfire Elemental triggers once for each event in which an opponent is dealt noncombat damage, regardless of how much damage that player is dealt.

Wildfire Elemental's triggered ability affects only creatures you control at the time it resolves. Creatures you begin to control later in the turn won't get +1/+0.

In a multiplayer game, if a source deals damage to multiple opponents at the same time, the last ability of Wildfire Elemental will trigger that many times.