No, James is not an auror. (You are maybe mixing him up with Frank Longbottom? Though in that case, Alice is an auror, too.) The only thing we know about him is that he is in the Order, just like Lily. That's without JKR's interview! She just confirmed that there is nothing more to their careers in her mind.

Are there many central male characters who are alive but unmarried and don't have children by the end of the series? Or any?

I think regardless of gender, a happy ending ideally includes kids for JKR.