In English the word "son" can only mean a boy. It is not that way in all languages. For example, in Italian a daughter can only be a girl but a son can be a girl or a boy. In English, you need to say "child" if you don't want to specify which it is. That's why Stephanie and JK have correctly answered your question.

Yes, this is still used. If a family has many children, saying "Middle son", would suggest there are at least three sons and we are talking about the person who is in middle of the boys in age. Girl 20, boy 19, Joe boy 17, girl 16, girl 14, boy 12, girl 10, Joe is middle son.

Even if there are more than three children in total, you could still say "middle son" if only three of the children are boys. But usually people only say "middle child" when they're talking about a family with exactly three children.