Sarulf, Realm Eater

It doesn't matter which graveyard the permanent is put into as long as an opponent controlled it when it last existed on the battlefield.

If Sarulf isn't on the battlefield as its last ability starts to resolve, you can't remove any +1/+1 counters from it, even if it had +1/+1 counters when it was last on the battlefield. No other permanents will be exiled.

If Sarulf doesn't have any +1/+1 counters on it as your upkeep begins, its last ability won't trigger at all. If the ability does trigger, it will check again as it tries to resolve. If Sarulf doesn't have any +1/+1 counters on it at that time, the ability won't do anything. No other permanents will be exiled.