Those are some great questions and an excellent conversation to have. Unfortunately I do not think I can add much but nonetheless I will opine! I have never and do not think about those issues much if ever, but:

0. I think so.

1. Yes but no more than males I do not think. Everyone has different strengths and weaknesses.

2. Sometimes yes. I can be pretty pushy in that regard if I think I am best suited for that role.

3. Absolutely no preference whatsoever. I want the best person and that choice varies in between men and women depending on the project.

4. Of course it is possible. But I do not think I am making arbitrary assumptions.

5. I hope so.

I have been lucky to have been surrounded throughout my life with men and women who are very strong, self-confidant, egalitarian and strong enough to speak out against those who are prejudiced in any way. They have not been over-reactionary "SJWs" but simply know when fair is fair and when it is not. It is odd that I grew up in a small redneck Southern Ontario hockey town with mostly white male friends that many could assume would tend to be chauvinistic and racist but that was the opposite of my experience. And i have been lucky enough to continue that through undergrad and grad school and into the workplace.

I was lucky enough to study in a program that was 50/50 and work in an area that is maybe 60/40 male. I have worked with good and bad male and female team leaders and hired men and women and gender has never played into my hiring decision (as far as I know). I am sure my experience is not universal but I have never heard any man put down a woman either directly or subtlety and I think I would clue in if I did. And I would say something. I certainly have outside of the workplace.

A couple of my good friends are stay at home Dads because their spouses have greater earning potential than they do and their parenting skills are as good as any. My male and female friends both get pissed when they hear someone say that "being a Mom is the hardest job in the world" since that minimizes the role of men in child rearing and perhaps "being a good parent is the most *important" job in the world" would be more accurate. Maternity and paternity leave is something that should be universal and equal. Both parents need to be directly and actively involved in their kids lives.

I don't know if my experience is unique or whether I am simply naive. It is hard to be objective about your own biases. But that is the way I perceive it.