Anonymous“If a person is dating or living with someone or even is raising kids with someone and not married, is it all right to say 'he's single'?”
On a census form, yes.
On a work-related form, yes.
In a social situation, no! In a social situation, the word "single" carries a strong connotation of "not attached, not involved, available." You would say something like "Technically, he's single" if asked whether he was married. If I were living with someone and I heard him saying in a social situation that he was "single," you better believe that he would be truly single very soon thereafter!