Ug, that sounds like a terrible experience overall. I’m hoping #4 works out for you!
For #1 and #2, reading about implicit bias might be interesting. Unfortunately, it is still a real problem in 2016 and in traditionally male areas in particular (e.g. women being assertive being interpreted as intimidating vs decisive https://www.fastcompany.com/3031101/the-future-of-work/the-new-subtle-sexism-toward-women-in-the-workplace)
As I’ve worked for more companies and teams, I’ve started looking at a job search more like dating in some ways. Your manager/company are the ones you will be spending huge amounts of time and making sure it is a good fit for both you and the company in terms of the work as well as the culture is really important. Asking a lot of questions about what is important to you as you did for #4 sounds great. Sometimes it’s hard to know the right questions to ask though since there are things that make sense to you but others may have totally different ideas like #3 in ways you never thought could happen.