If lethal damage is dealt to Screaming Nemesis, its last ability still triggers.

If Screaming Nemesis is dealt damage by multiple sources at once, such as by two creatures blocking it, its last ability triggers once and one target is dealt that much damage.

Once Screaming Nemesis's last ability causes it to deal damage to a player, that player won't be able to gain life for the rest of the game. It doesn't matter if Screaming Nemesis remains on the battlefield or not.

Spells and abilities that cause a player affected by Screaming Nemesis's last ability to gain life still resolve. That player won't gain life, but any other effects of that spell or ability will happen.

If an effect says to set a player's life total to a number that's higher than their current life total while they're affected by Screaming Nemesis's last ability, their life total won't change.