If the creature goes to the graveyard and then moves to exile, then it counts as dying. However, if it goes to exile instead of the graveyard, then it does not count as dying. If a creature dealt damage this way would die this turn, exile it instead. If an event is replaced, it never happens.

Does exiling a creature kill it?

Exile is another event entirely, and will not trigger "dying" abilities. However, if the card only cares about a creature leaving the battlefield, then it will trigger.

Does sacrificing a creature count as it dying?

Yes you can . Dying is a keyword that means going from the battlefield to the graveyard. This includes sacrifice.