
I think he's dressed as a girl because they don't want two possible heirs. If it was made public that he was a dude then that'll give him the change to surpass the "main" son which is a big no no. Also cause the mother will try and kill him cause of that.
Spoilers
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The purple hair dude knows that he's a guy and is a massive weirdo I my opinion

Also here is the link for the raws
ヾ(❀╹◡╹)ノ~
https://funbe.cx/모시던_아가씨가_도련님이_되어버렸다_22화.html

I bet 100 dollars that the heroine of the story’s gonna be a bitch. She’s for sure going to plan several ways to break up the Fl and the Li. Maybe by starting a rumour, poison, and kidnapping??

Short answer: no. I can't read Korean but from the raws, the heroine desperately wants to be friends with the FL, that much is obvious. She tried back in school but it didn't work so well. Now she's completely enamoured with the FL to the point of being jealous of the ML. Other than a few dark expressions of jealousy, she's shown to be an upstanding person. The real bad guy here is the red head that was talked about a few chapters ago. That guy is crazy aggressive.
I'm so disappointed wtf