Each time a creature dies, check whether Dread Slaver had dealt any damage to it at any time during that turn. If so, Dread Slaver's ability will trigger. It doesn't matter who controlled the creature or whose graveyard it was put into.

If Dread Slaver and a creature it was blocking or blocked by both die in combat, Dread Slaver's ability will trigger.

Dread Slaver will return if it somehow dealt damage to itself and then dies.

The card will return to the battlefield under your control only if it's still in the graveyard when the ability resolves. If it's not (perhaps because an ability like undying has already returned it to the battlefield), nothing happens.