I haven't played a pickpocket in a long time but I can answer some of your questions.

Counterfeit lets you create a fake copy of an item. Uses include stealing an important potion from somebody, counterfitting it, and then planting the counterfeit back onto them. Then when they go to use it at a critical moment they are in trouble. Also it could be a way for somebody to not know they were robbed. Steal their weapon, counterfeit it, plant it back onto them. They don't know their weapon is gone. Devious people could come up with more ideas.

Fence used to work like this (unsure if it still does): You have an item you can't sell for whatever reason (shopkeepers have no money, in wrong town and need cash, etc.). You fence the item and it gives you money for it, but only a fraction of the worth. It has a timer so you can't just fence everything you have.

Most classes you can solo level to 20 without too much trouble if you are patient and look around for good areas or opportunities and incorporate quests/obs exp/etc. Thieves are not particularly good at solo-leveling. I'd say after a certain rank (30 at the very latest) you would have a hard time solo leveling at all.