The cost reduction applies only to generic mana in the total cost of black spells you cast.

While you control The Darkness Crystal, abilities that trigger whenever a nontoken creature an opponent control dies won't trigger because that card is exiled instead.

If The Darkness Crystal leaves the battlefield at the same time as one or more nontoken creatures an opponent controls would die, those creature cards will be exiled and you'll gain 2 life for each of them.

To determine the total cost of a spell, start with the mana cost or alternative cost you're paying (such as a flashback cost), add any cost increases (such as kicker costs), then apply any cost reductions (such as that of The Darkness Crystal's first ability). The mana value of the spell is determined by only its mana cost, no matter what the total cost to cast that spell was.

If a creature token an opponent controls dies, it goes to that player's graveyard as normal before ceasing to exist.