Does equipment get destroyed when creature dies?

If an equipped creature dies or gets bounced, the equipment stays in play, and you can equip it the next time you can play a sorcery.

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Are auras targeted?

113.1b Aura spells are always targeted. These are the only permanent spells with targets. An Aura's target is specified by its enchant keyword ability (see rule 702.5, "Enchant"). The target(s) are chosen as the spell is cast; see rule 601.2c. Do you control auras MTG? You control auras that you cast, even if you put them on your opponent's permanents. Changing control of a creature doesn't change control of anything attached to it.

Then, can you enchant a creature you don't control?

It doesn't matter who controls the permanent that the Aura is enchanting. A permanent's controller is whoever put it into play unless the spell or ability that put the permanent into play states otherwise. Can you sacrifice an indestructible creature? Description. Indestructible permanents can still be put into their owner's graveyard by other means, such as by the "legend rule", by being sacrificed or (in the case of creatures) having zero or less toughness. They can also be removed from the battlefield by being bounced or exiled for example.

Consequently, can you destroy darksteel mutation?

The creature is indestructible and is not destroyed. At the same time, [[Darksteel Mutation]] is destroyed. By the time the Darksteel Mutation is destroyed, the effect that is destroying it has resolved. So, while the creature is no longer indestructible, it is still on the battlefield.