I think that in English, there is no 'right' answer for a negative question. Some people use one way, some people use another. So we typically do as you have done, and add additional information to make it clear. Yes, 'Is he not happy?' is OK. I think that 'Isn't he happy' would be slightly more common, but neither is wrong.

B is a much safer reply. "Isn't he happy?" "Unfortunately, yes" That would be very confusing. Whether technically right or wrong, no one would say that.

Gary gave a good answer to your second question. As far as your first question, I would say B is good, but I would usually say "unfortunately not," or a bit more formally / clearly, "unfortunately, he's not." Answer A is a common mistake Chinese, Russians and others often make when speaking English.