This also applies to the original fairy tale as well. Did Rapunzel ask who her father was and what he looked like? Did Gothel tell her he died?
No, in the original Grimm's fairy tale (which is very short; a full English translation is here), Rapunzel never asks about her father. Nor, for that matter, does she ask about her mother in the story, since it appears that Rapunzel is aware that Gothel is not her mother. (She addresses her by name, and rather formally, not by a familial term of affection.)