J'onn has never met Rene or Dinah so he couldn't have given them his memories, same with Nash for the most part, I saw a vision of Nash under Central City freeing Anti-Monitor. J'onn was never there to witness that event, even if he heard about it, that vision wouldn't have shown up. Superman doesn't remember having 2 Kids and Lena seems to have her old memories. ALSO in a promo for Green Arrow & The Canaries, Mia gets ALSO of her memories back despite the merge Earths and timeline changes and J'onn is not there so I don't believe in that theory.
Pre-Crisis and Post-Crisis would be better than Prime because Prime means center of importance of first of importance, that's why Earth-Prime most likely name the way it is.