Mordred’s dad is her dad. Artoria did not give birth to Mordred she only provided the sperm.

Mordred’s aware she was female but because of Morgan’s grooming/abuse she was taught her femaleness was something she should be ashamed of. It’s why she’s both extremely hostile to people calling her a woman but also wants to be acknowledged as a girl.

She does have potatoes brains because she’s like mentally several years younger then her body because Morgan made her grow much faster then her actual age. You can see this is Apo because she behaves very childishly (throwing temper tantrums because she’s bored, and chasing around a cat on all fours).