I see you have a struggle which isn't totally answered and I'll try to explain it once again, and give an answer which I think is right. Please correct me if I'm wrong.
The first problem is answered I guess, but the second problem you encountered is a little different. You suppose you have a creature with Sleep Paralysis enchanted to it. Of course, you do not like this at all and you think your creature is better off in your own graveyard. You have a Certain Death in hand and you cast it with your own creature as target. It does resolve. What happens with the life totals of the players?
110.2. A permanent's owner is the same as the owner of the card that represents it (unless it's a token; see rule 110.5a). A permanent's controller is, by default, the player under whose control it entered the battlefield. Every permanent has a controller.
608. Resolving Spells and Abilities
608.1. Each time all players pass in succession, the spell or ability on top of the stack resolves. (See rule 609, "Effects.")
608.3. If the object that's resolving is a permanent spell, its resolution involves a single step (unless it's an Aura). The spell card becomes a permanent and is put onto the battlefield under the control of the spell's controller.
608.3a. If the object that's resolving is an Aura spell, its resolution involves two steps. First, it checks whether the target specified by its enchant ability is still legal, as described in rule
608.2b. (See rule 702.5, "Enchant.") If so, the spell card becomes a permanent and is put onto the battlefield under the control of the spell's controller attached to the object it was targeting.
111.2. A spell's owner is the same as the owner of the card that represents it, unless it's a copy. In that case, the owner of the spell is the player under whose control it was put on the stack. A spell's controller is, by default, the player who put it on the stack. Every spell has a controller.
Because your opponents casts the enchantment doesn't mean he controls the creature (exceptions for cards like lay claim). You are still the controller of the creature in this example, which means you both lose and gain 2 life, the creature is moved to your graveyard and the aura is moved to the opponents graveyard.
In the case the aura was a lay claim and not a sleep paralysis, your opponent loses 2 life and you gain 2 life, the creature is moved to your graveyard and the aura is moved to the opponents graveyard.