I actually like to think she has all the parts needed lolol
after all, she might just be having a hard time connecting the euphemism to the body part, and/or isn't quite aware of people being self conscious about that aspect in particular
just because you physically have a body part doesn't mean you're aware of all the societal implications or common pressures of what you compare to others and how, especially since she wasnt quite raised as such ( ̄∇ ̄") and if by chance she has a hard time with euphemisms in the first place, she might have to ask someone else for clarification... rip her father LMAOOOOO

About Ice Dragon King's dragon.
Low-key spoiler? Or not? Idk
I believe, FL's "male form" only looks beautifully masculine, not literally. After all, she didn't understand her husband's snakey inferiority. If she has the things needed, she wouldn't need to ask her poor father and cause him to become bedridden due to overlaughi-, ehem, shock.