The characters around him treat him as a man and Oden was so. Call him/her however you want, we have reasons supporting both choices.
"Talk about mental disorder", suggesting that transgenderism is a mental disorder, nice.
Every mental disorder has a line of thinking, so I don't get your point. It is obvious why he's calling Momo his son, it doesn't make it less disturbed. This isn't just about "living up to her ideal which is Oden", Yamato stole Oden's persona without even caring about the actual circumnstances of Wano's opening, be them the Scabbards returning as Toki suggested and claiming the country while Momonosuke becomes the next legitimate shogun.
Regarding your second point, and replying to this too:
Whitebeard asks Ace to become his son, first of all, so he doesn't assume him to be his son to begin with, and second, that's how his crew works; Marco explained very clearly why they all treat him as a father even if they aren't a blood family because their caring dynamics. In Yamato's situation, on the contrary, he's assuming by default that Momonosuke is his son without asking him first nor having any relationship with him because he has convinced himself that he's Oden "so of course that kid is my son, is the only logical conclusion!", which is why it is disturbing. For the Whitebeard countexample to work he should have convinced himself that he's Roger and therefore treat Ace and Ace alone as his son because he was Roger's biological son. Completely different scenario.