I've heard this (similarly "a Chinese"), and I have the sense that it is getting more common, though I have no actual evidence for that. I don't like it – not because it's offensive or anything, but just because it seems like bad English. It's peculiar that some country adjectives double up fine as nouns referring to someone from that country (German, Italian, Iraqi, etc.), others have separate forms (Dane, Swede, Turk, etc.), and yet other countries, such as Japan and China, seem to lack a single word for a person of that nationality.I'm not aware of anyone who refers to a Japanese person as "a Japanese"
Apparently, in second sentence "if she were my mother." is "a non-factual condition", and that is S/MI don't think you understand what the subjunctive mood is.
I'm not aware of anyone who refers to a Japanese person as "a Japanese"