Welcome to the forums!
Yes they can shop. They get money multiple ways. By working, or by collecting things, selling things that they make, really how they make money is practically an endless list!
Well going bankrupt is hard, but I guess it could be done. If they do not have the money to pay the bills, the repo man will come and repossess their items.
Buying stuff for their house is as easy as going into build/buy mode.
If you have the elixir shop yes they can buy potions. In the skill Alchemy, there is a Potent Cure Potion that will cure them from whatever they have become and turn them back into normal sims.
Giving tips I don't believe takes any money from them, but yes buying things takes their money. Sometimes when you have free will on high, yes they will act silly lol. That's part of the awesomeness that is the sims though!