Armadio dei Costumi

A creature that is equipped is considered modified no matter who controls the Equipment that's attached to it.

A creature with a counter on it is considered modified no matter what kind of counter it is or which player put it on that creature.

An Aura controlled by an opponent does not cause a creature you control to be modified.

If Costume Closet has left the battlefield or has no +1/+1 counters on it by the time its activated ability resolves, you won't put a +1/+1 counter on the target creature. If the creature becomes an illegal target or can't have a +1/+1 counter put onto it for some other reason, you won't remove a +1/+1 counter from Costume Closet.

Once Costume Closet runs out of +1/+1 counters, it remains on the battlefield. However, activating its second ability won't do anything.

The +1/+1 counters on Costume Closet won't affect it unless it somehow becomes a creature.