I'm also curious about her father, and hope that her memories of him have some ongoing relevance to her character and that he was a character in the fullest sense. Her parents in previous versions are pretty much standard-issue Krytonian futuroids, aren't they? I mean, back when I was paying attention (I admit again, it was a while ago) the main way you could tell one Authoritative Kryptonian Male Scientist from another was by the symbol the artist drew on their shirts and whatever the colorist did with their hair. Evidently succession to leadership on the Science Council or whatever is based on a pattern-baldness-and-beard-growing competition that's only open to men of seventy years or older.
Her parents were actually developed a bit in the previous iteration especially her mother who had become the leader of the short lived New Krypton.