If someone casts an aura on my creature, do I still control the creature?

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.

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.*

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.

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.

The only way an aura or equipment can change control of a permanent is if it specifically states "you control enchanted/equipped permanent/creature/land/artifact/enchantment"

Some spells and abilities let you gain control of a permanent

Sleep Paralysis does not change control of permanents. Lay Claim is an example of an Aura that changes control of a permanent. It has

You control enchanted permanent.

This ability transfers control of the enchanted permanent.

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Most of the time, this means the card will move from your opponent's side to yours.

Say you have a creature to which you have a Bone Saw attached, and your opponent attaches Lay Claim to your creature.

Your opponent controls the creature, so it moves to their side, and they can attack with it and use its abilities (but you can't). You can't sacrifice it to Fling (but they can), and they would lose life if it's targeted by Certain Death (and you wouldn't). It even gets the +1/+0 from Bone Saw.

However, you still control Bone Saw. As an Aura or Equipment, it physically stays with the creature to which is attached. Only you can use its activated ability (say to equip Bone Saw to a creature you still control).

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But for Auras or Equipment attached to other cards, the controller changes but it doesn't move.

Say you have a creature to which you have a Bone Saw attached, and your opponent attaches Lay Claim to Bone Saw (not the creature).

You control the creature, so it stays on your side, and you can attack with it and use its abilities. You can sacrifice it to Fling, and you would lose life if it's targeted by Certain Death. It even gets the +1/+0 from Bone Saw.

However, your opponent controls Bone Saw. As an Aura or Equipment, it physically stays with the creature to which is attached. Only they can use its activated ability (say to equip Bone Saw on one of their own creatures).

Sleep Paralysis does not change control of your creature. It just taps it and prevents it from untapping, which certainly does make it a lot less useful, but it's still yours.

The kind of thing you have to worry about will explicitly say "control", like the classic Control Magic, which is an aura that reads simply:

Enchant creature

You control enchanted creature.

If your opponent plays that on your creature, then yes, they'd control it. In that case, you wouldn't be able to use Fling with that creature (but they would!), and Certain Death would deal them damage.