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

You must still pay all costs and follow all normal timing rules to play a card this way. For example, you may play a land this way only during your own main phase while the stack is empty, and only if you have not yet played a land this turn.

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.

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