It's difficult to say. It seems to come about due to specialisation of social roles, and the creation of hierarchies of power and influence, as humans moved from being a hunter-gatherer to a more agrarian society.
It's hard for me to know what you mean by "non binary type stuff," but if you mean, "do you believe that gender should be treated as largely irrelevant to social roles?" my answer would be yes.
I think what you're picking up there is probably more our society's tendency to default to understanding generic terms as masculine, rather than the word "kid" being particularly gendered.
No no no. I completely disagree. Women aren't told to dress modestly more than men, because men are more visual; it's because men are more socially dominant. I don't agree with every point
this article makes, but I think the basic thrust of the argument is sound (and well worth considering).