Nope. In every professional environment (And most academic) I've been in the company of strong leaders of both genders. My office is probably 70-80% female, and most of them hold several more degrees than I do.
Maybe 4 and 5. When I was selling insurance I didn't really have coworkers, in school I was just as likely to be let down by female group members as male, and had to take the lead most of the time anyway because of generalized apathy. #4 - I try my best to only judge other people by the actions that I have directly observed. Sometimes by the way that someone I care about relates to them, but I try to take secondhand news with a good measure of salt. #5 - I asked this one too much (Or a variation on it) and got myself into therapy. Now I try and be mindfully loving and not worry about it much beyond that. And I was the person fixated on binaries yes.