How much expenses do the doctors have to pay?

The short answer is- a lot. In the US, medical school tuition is about $30-50 thousand per year x 4 years, plus living expenses. Most people take out loans to pay for this. You'll need to take 3 licensing exams in order to graduate, and one more after that, which will run you several thousand dollars. It also costs several hundred dollars to apply for residency, and you are responsible for the travel costs for interviews. You do get paid during residency, although not much (average $50,000 per year). It doesn't end after residency - you then take your specialty board exams for about $2000, with renewal every 10 years, and pay for maintenance of certification and continuing education. A DEA license (so you can prescribe drugs) costs $700, and some hospitals will also charge you for credentialing (this is the paperwork involved to allow you to work in a hospital). There is also state licensure (variable cost and renewal frequency depending on the state/how many states you are licensed in). That said, once you are done training you a pretty much guaranteed a 6 figure salary, so it is possible if you are smart with your finances to pay of your debt and manage all the costs. For most, the career is rewarding enough that this is all worth it. Unless you are in a very high pay specialty, you will not not be rich, but you'll be comfortably middle class.

To answer your second question, there are a number of combined residency programs where you can get training in two specialties at once. A lot of these are combined with internal medicine or pediatrics (more broad specialties) with other specialties. Check out the links below to see what combined residencies are available. Currently, there are no combined Psychiatry/Dermatology residencies (they would have to be done separately).