2. You answered your own question in your parenthesis. As for your second question, if they wouldn't listen to Mulan, why the hell would they listen to any other woman?
4. You're an idiot. 1) Shang wasn't with them when the guys dressed as women, 2) Yes, Shang had problems trusting Mulan; she outright addressed this in the movie for crying out loud ("You said you'd trust Ping. Why is Mulan any different?"), 3) "Would it have been degrading or undignified?" You just figured out why some people think crossdressing jokes are funny, which means that this scene isn't the progressive statement you seem to think it is.
And really, you're watching a movie that takes place in ancient China, and the things you choose to latch on to are either inconsequential bullshit, things that have already been established as sexist in the culture itself, and a joke. What about the scene where the matchmaker is telling her she has to be silent to please her in-laws? Or the scene where Shifu says that she needs to hold her tongue in a man's presence? Or the fact that she'd be killed for being a woman in the army?