Can my oponnent regenate his creature if it would die from my {Mutilate}?
Can I activate and pay the cost of regeneration in {Eater of Hope} (pay mana, sac a creature) if its not being destroyed?
What activating the regenerate ability does, is create a "shield" that is used the next time a creature is destroyed. This can be from receiving lethal damage (more damage then the toughness of the creature), or getting any damage from a creature with deathtouch, or from a spell that says so. The shields last until end of turn, or until they are needed.
So even if there is no imminent destruction, you can create as many shields as you want/can pay for.
If a creatures toughness is 0, however, regeneration will not save it. It is going to the graveyard.
Thank you homies! So if its destroyed by {Sudden Shock} it cant be responded to and its dead because of the Split Second, correct?
very true. thanks again!