Responses
Pretty sure he knows. I think he calls him she because he doesn't want other people to know. Whenever he adresses Yu-er as she it's in quotations marks like "she" while everyone else's weren't in quotation marks, to me meaning be knew, but wasn't disclosing it probably for political/personal reasons
I think since the prince had sex with the Mc a lot he already knows he's a make, the doctor also knows and the servant might know since he sees him in bed after the prince leave and he applied medicine to him once. Plus there's the pronouns thing and all..
Its safe to assume the important characters already know he's male, maybe the prince sometimes addresses him as she out of habit, who knows