Can you gain control of an aura?

You can do that, but generally speaking nothing will change. Most auras (like Indestructibility) give the creature they enchant an ability. It doesn't care who controls the aura only what it is enchanting.

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Can you steal auras MTG?

Yes, most of the times it doesn't matter who controls the aura and who controls the creature. There are a handful of exceptions, e.g. Cartouche of Knowledge which can only enchant a creature you control; if you'd steal one of them it would stop enchanting a legal target and be put into its owner's graveyard. Correspondingly, can you enchant a tapped creature? Nope, you can enchant a tapped creature just fine. If it said "enchant untapped creature", it would have to be an untapped one, but you can enchant a tapped one. When the ability triggers and tries to tap the creature, the game sees that it's already tapped and goes "Oh well, never mind".

What happens to stolen permanents when a player dies MTG?

killsdazombies asked: If I gain control of another players permanent, say with something like blatant thievery, and then I die, what happens to the stolen permanent? It will go back to the player who controlled it before you did. Keeping this in consideration, where do permanents go when a player dies? any effects end, permanents owned by other players are returned to them. cards they exiled remain in exile.

Accordingly, what happens to stolen permanents when the player dies?

The big take-away is this: as soon as you die, all your stuff leaves the game -- then, after that, if you would still control anything (e.g. a permanent you stole from someone else), that thing is exiled; any triggered abilities you would own don't occur.