"Keine Freundin, keine Frau?"
The cruel side of Duolingo playing with the internet folks' feelings :(
Is it possible to interprete/translate it as "No ones girlfriend, no ones wife?"?
No. In your sentence, "No one" would translate to "Niemand" (though in some other gramattical case -- I will not attempt to translate "No one's girlfriend" as I'd likely make a mistake, my German isn't good enough for that).