Some descend triggered abilities include intervening "if" clauses (i.e. "if you have [four or eight] permanent cards in your graveyard" in the middle of the ability). Each of these abilities checks your graveyard at the moment it would trigger to see if it does. If you don't have the required number of permanent cards in your graveyard at that time, the ability doesn't trigger at all. If it does trigger, it will check again as it tries to resolve. If you don't have the required number of permanent cards in your graveyard at that time, the ability won't resolve and none of its effects will happen.

Transforming Matzalantli doesn't cause it to leave the battlefield. It also doesn't cause it to become untapped.

Cards with the ability word "fathomless descent" have abilities that care how many permanent cards are in your graveyard.

The Core's activated ability is a mana ability. It doesn't use the stack and can't be responded to.