Nazar's second ability triggers just once for each life-gaining event, whether it's 1 life from Dazzling Angel or 4 life from Apothecary Stomper.

Each creature with lifelink dealing combat damage causes a separate life-gaining event. For example, if two creatures you control with lifelink deal combat damage at the same time, Nazar's second ability will trigger twice. However, if a single creature you control with lifelink deals combat damage to multiple creatures, players, planeswalkers, and/or battles at the same time (perhaps because it has trample or was blocked by more than one creature), the ability will trigger only once.

If you gain an amount of life "for each" of something or "equal to the number" of something, that life is gained as one event and Nazar's second ability triggers only once.

In a Two-Headed Giant game, life gained by your teammate won't cause Nazar's second ability to trigger, even though it caused your team's life total to increase.

If Nazar isn't on the battlefield as its last ability resolves, you can't remove three feeding counters from it, even if it had three or more feeding counters on it before it left the battlefield. You won't draw cards or lose life.