"You" refers to the controller of Curiosity, which may be different from the controller of the enchanted creature. "An opponent" refers to an opponent of Curiosity's controller.

Any damage dealt by the enchanted creature to an opponent will cause Curiosity to trigger, not just combat damage.

Curiosity doesn't trigger if the enchanted creature deals damage to a planeswalker or to a battle.

You draw one card each time the enchanted creature deals damage to an opponent, no matter how much damage it deals.

If you control Curiosity and it's enchanting an opponent's creature, you won't draw a card when that creature deals damage to you. The creature has to deal damage to one of your opponents for the ability to trigger.