A "cheap" lawyer is not what you need in a divorce. What you want to find is a lawyer who is competent that you can afford. What you want to do is talk to some lawyers, explain your current situation, and see what they would charge to represent you. Go ahead, lawyers understand that people going through a divorce do not have unlimited amounts of money.
No, you paid for your unemployment compensation while you where working or rather your employer did. You do not have to pay it back and it will have no adverse affect on your credit history or when you apply for any positions in the future.
This is a common question. The answer is to look at your Marital Settlement Agreement and the Findings of Fact and Conclusions of law. It will say in those documents. If it does not say you have to pay for half of those kinds of things or that he has to ask your permission first, then you do not have to pay.
If you incorporate, such as a single-member LLC, you can avoid personal liability if anything goes wrong. You are free to contract with vendors, but if you do so and things go wrong you will be personally liable to them and, perhaps, any people that might be injured. Speak to a business attorney. It may cost a little money but if something goes wrong it could cost you a whole lot more. Good luck!