Does the level of the pickpocket skill determine how much gold I can steal

Most dungeons are cleared when you have killed all important inhabitants, and as a result of doing that, you have seen the whole dungeon. The game doesn't force you to loot stuff (e.g., Werewolf form can't loot) so it comes down to just killing; you don't have to do your quest.

A victorious sound will play once you clear the dungeon, and the ambient sound will stop.

If you don't kill all important inhabitants, inhabitants might respawn and the dungeon will not be seen as cleared. Another occasion where inhabitants respawn in a dungeon is when you start a new quest that involves that dungeon; however, it won't change the cleared state of a dungeon.

There are reports that some dungeons don't get cleared, or are cleared a different way. Some report that whatever they try to do, the dungeon doesn't get cleared; this might be because they still have a quest to do in the dungeon. Other report that a dungeon gets cleared after looting a chest or learning a new dragon shout word. Please note that not every dungeon has a word wall.

It's based on the value of theitems you steal.

Easy way to check this: Go to a trainer, pay them for training 1 level of a skill. Then pickpocket the money you paid them back. Then pay them for training 4 levels, and pickpocket that money back all at once. You'll see a much greater skill increase.

(Incidentally, you can use this 'exploit' to reach a fairly high level before even leaving the first village in the game.)