The vast majority of women will not continue dating a man who earns less than they do. Two thirds of young women in Germany expect their future partners to take care of them financially.
So for men, earning money and status is absolutely essential.
See also: https://www.theguardian.com/lifeandstyle/2016/jul/02/a-lette...
(2) What makes you think it wouldn't? After all, it affects everyone in society. And motivation is a pretty powerful force, it is basically how our entire economy is structured.
See also:
https://economix.blogs.nytimes.com/2009/11/18/money-gender-a...
"...it typically takes a lot less money to get women to say they are satisfied with their work than it does to get men to say it."
"Women were more likely to tell PayScale that say they find their jobs “very meaningful” than men were, with 35 percent of women and 27 percent of men describing their jobs this way."
So women have more freedom to find meaningful jobs. Men less so.
For free market choice on which jobs pay more -- I think this one is pretty clear. Do you think differently?
As for biological preference, I don't think it takes into account the average pay at all. Career path is usually chosen at a younger and more idealistic age, and probably more importantly - poorer countries have women overriding their preferences and going into higher paid lines of work, while richer countries let women do what they want. As per this very study. In the case where money doesn't matter because your family is rich, biological preferences become more important and people stop choosing based on average pay. So the biological differences seem to explain it really well.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3030621/
And of course, far more studies that have been going on for decades.