If an exhaust ability of a permanent is activated, and then that permanent leaves the battlefield and returns to the battlefield, it becomes a new object so its exhaust ability can be activated again.

The creature you target must have a +1/+1 counter on it when the ability goes on the stack at the beginning of combat. You cannot put the counter on it in response.

Exhaust abilities can be activated any time you could normally activate an ability.

If an ability triggers whenever you activate an exhaust ability, that ability resolves before the exhaust ability resolves.