If my opponent steals a creature from me with Control Magic, I could steal it back by casting another Control Magic on it and (I think due to timing?) I would control the creature.
Yes, but not due to timing. CR 116, Timing and Priority, is a section of the rules that covers when players can cast spells and activate abilities.
In this scenario, you have two continuous effects (one created by the first Control Magic, and one created by the second Control Magic) trying to change control of an object. This is handled by CR 613, Interaction of Continuous Effects.
Both of the effects are applied in layer 2 (Control-changing effects)[CR 613.1b], and neither is a characteristic-defining ability, so they are applied in timestamp order[CR 613.2], so the last effect created wins out in this case[CR 613.6].
613.1. The values of an object’s characteristics are determined by starting with the actual object. For a card, that means the values of the characteristics printed on that card. For a token or a copy of a spell or card, that means the values of the characteristics defined by the effect that created it. Then all applicable continuous effects are applied in a series of layers in the following order:
613.1b Layer 2: Control-changing effects are applied.
CR 613.2. Within layers 1–6, apply effects from characteristic-defining abilities first (see rule 604.3), then all other effects in timestamp order (see rule 613.6). Note that dependency may alter the order in which effects are applied within a layer. (See rule 613.7.)
613.6. Within a layer or sublayer, determining which order effects are applied in is usually done using a timestamp system. An effect with an earlier timestamp is applied before an effect with a later timestamp.
613.6a A continuous effect generated by a static ability has the same timestamp as the object the static ability is on, or the timestamp of the effect that created the ability, whichever is later.
613.6c An object receives a timestamp at the time it enters a zone.
If instead I cast Steal Enchantment on the Control Magic, does the "You" become "me," and would I now control the creature?
Yes.
"You" refers to its controller[CR 109.5]. Since you control the enchantment, and since it gives its controller ("you") control of the enchanted creature, you control the enchanted creature.
CR 190.5. The words “you” and “your” on an object refer to the object’s controller, its would-be controller (if a player is attempting to play, cast, or activate it), or its owner (if it has no controller). For a static ability, this is the current controller of the object it’s on. For an activated ability, this is the player who activated the ability. For a triggered ability, this is the controller of the object when the ability triggered, unless it’s a delayed triggered ability. To determine the controller of a delayed triggered ability, see rules 603.7d–f.