How to deal with an unprepared professor?

One important thing about higher education is that in general nobody else than you takes responsibility for your learning. So if you decide to learn the material from books/other resources this should be fine. However, teachers/lecturers are still responsible to deliver good lectures. So the teachers set the stage to learn, but you can learn in any way you like.

That said, it still makes sense to try to improve the teaching. You write that the problems are external to the professor. This should make it easier to approach him. For example you don't have to say "I would like more explanation and better answers to our questions" but you can ask for additional material where you can find answers to your questions.

However, if you think that the assignment of this professor to this class was in general a bad decision (due to, for example, lack of expertise, lack of time, too many other commitments…) you can bring this up to people in the department who are responsible. However, it is important to focus on facts and describing the situation in neutral, non-judgemental terms.

If you aren't comfortable bringing this up to the instructor, you should definitely bring this up to someone in the department, such as the under/grad coordinator or chair.

Like you said, you paid for this class. Things like this can slip by without the department ever being aware of it but I would hope that they would take this very seriously.