Abilities that trigger whenever a creature an opponent controls dies won't trigger unless that creature is a token (see below).

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

You can't sacrifice Kalitas to activate the last ability, even if it's somehow become a Zombie.

If Kalitas dies at the same time as creatures your opponents control, those creature cards will be exiled and you'll get that many Zombies.