Not hugely so. Teaching isn't paid megabucks but that's partly because it's a market for lemons - it's hard to tell a good one from a bad one (and people don't even agree in what it means to be educated, are facts or "critical thinking" more important, how about discipline vs temporary comfort) so there's no high paid super stars.

There is a stereotype that teachers are low paid. Somewhat .... but there's a slight premium on doing meaningful work.

The whole premise that women are paid far less is kind of wrong anyway (or at best another outdated stereotype).

Childless men and women make about the same amount.

Women with children work fewer hours and share finances with men who work more hours, and apparently this is an injustice.

Could you be more specific? I don't know what you're referring to.