If I lose control of an equipped creature, does the equipment stay attached to it?
You are correct. The equipment stays attached to the stolen creature, but you still control it and may re-equip it to a different creature that you control.
Here are the rules for equipment (emphasis added):

301.5. Some artifacts have the subtype “Equipment.” An Equipment can be attached to a creature. It can’t legally be attached to an object
that isn’t a creature.
301.5a The creature an Equipment is attached to is called the “equipped creature.” The Equipment is attached to, or “equips,” that
creature.
301.5b An Equipment is cast and enters the battlefield just like any other artifact. An Equipment doesn’t enter the battlefield attached to
a creature. The equip keyword ability attaches the Equipment to a
creature you control (see rule 702.6, “Equip”). Control of the
creature matters only when the equip ability is activated and when it
resolves. Spells and other abilities may also attach an Equipment to a
creature. If an effect attempts to attach an Equipment to an object
that can’t be equipped by it, the Equipment doesn’t move.
301.5c An Equipment that’s also a creature can’t equip a creature. An Equipment that loses the subtype “Equipment” can’t equip a creature.
An Equipment can’t equip itself. An Equipment that equips an illegal
or nonexistent permanent becomes unattached from that permanent but
remains on the battlefield. (This is a state-based action. See rule
704.) An Equipment can’t equip more than one creature. If a spell or ability would cause an Equipment to equip more than one creature, the
Equipment’s controller chooses which creature it equips.
301.5d An Equipment’s controller is separate from the equipped creature’s controller; the two need not be the same. Changing control
of the creature doesn’t change control of the Equipment, and vice
versa. Only the Equipment’s controller can activate its abilities.
However, if the Equipment grants an ability to the equipped creature
(with “gains” or “has”), the equipped creature’s controller is the
only one who can activate that ability.

And here's the exact wording of the equip ability (emphasis added):

702.6a Equip is an activated ability of Equipment cards. “Equip [cost]” means “[Cost]: Attach this permanent to target creature you
control. Activate this ability only any time you could cast a
sorcery.”

So, essentially, only the equip ability itself specifies &quot;creature you control.&quot; If the equipment is already attached, the only restrictions are:

The equipped permanent must still be a creature (301.5).
The equipment cannot itself be a creature (301.5c).
The equipment can't be attached to a creature with protection from it, due to the definition of protection (702.16).

Creatures changing control doesn't violate that.