Thank you for being civil. However, I think you are mistaken about some of your facts and I can back all that up
Firstly better pay is NOT a myth, many conservative commentors have made the same claim you have and indeed it is true that some studies have used the methodolgies you have described and have come to less than accurate conclusions. Fortunately, there have been MANY MANY studies on this looking at lots of different factors and each shows women make less objectively. Oh, and for younger women it is still true which is especially alarming given that my (milennial) generation has more educated women who should make more but still don't!
sources:
http://www.aauw.org/research/the-simple-truth-about-the-gender-pay-gap/
http://time.com/2870940/millennial-women-are-still-getting-paid-less-than-men/
Despite your one example, and of course there are exceptions, women have a harder time getting promotions and it is not always their choice. Aside from this Harvard Business Review article go look at the CEOs and board of directors of 90% of major corporations, I guarantee you they will be at least 3/4 men
https://hbr.org/2010/09/why-men-still-get-more-promotions-than-women
For politics I really don't think the reason boils down to women are too interested in clothes and makeup to be serious, although female poiticians do suffer from this more. However, my evidence would be that there are simply waaaaaaaaaaaaaaaaaaaaaaay more men in politics than women and again this is more than choice:
https://www.american.edu/spa/wpi/upload/2012-Men-Rule-Report-final-web.pdf
"Women tend not to support other women in business, and women tend not to want those high powered jobs because they come with lack of flexibility, high stress, extra responsibility, etc." Evidence?