I personaly think that her father is dead, because as she was talking with Loki about the time's arcana in chap 5, Loki has been refering to her father in past: "he was this clan's descendant" For this reason I believe he's dead, but it's possible that the author will use him when the right time comes, as there was nothing clearly said regarding this character.
To answer the other question, I think it's possible he met him, but just as a little child. Otherwise, he would tell a lot about him to Nakaba, I'm sure.
The question which bugs me is why weren't Loki's parents ever mentioned and how old is he, for god's sake? In those memories of her mother dying, Nakaba is still a cca 3-4 years old child and he is a young adult already, mature enough to take care of her thoroughly.