Is drawing multiple cards an atomic action?
Spiteful Visions would trigger once for each card drawn, so if you cast Divination to draw 2 cards it would trigger twice and you would be dealt 1 damage for each trigger, and CoP:Black would need to be activated twice to prevent all the damage. Anything that triggers off of this damage would then trigger once for each time the artifact triggered. 

For Tomorrow it would not trigger because it does not contain the word "Draw", if it doesn't specifically say "Draw" it does not count as drawing cards they are just put into your hand.