I'm glad to hear that we can find some middle ground concerning the first point.
Concerning the second point, I can elaborate on why such evidence contradicts the claim the societal gender norms forces women into undesirable roles. I do not disagree that Scandinavian countries have their own culture, but instead that this culture has gone further than any other to remove gender roles and fight stereotypical normalcies. I did note that gender differences among various industries has grown in such societies. This is opposed to what was hypothesized to have happened. I do not think that such choices are entirely based on biology. However, such choices are proving to make women happier on average. It would make more sense that men are pressured into undesirable roles since they are less happy with those roles.
In regard to the third point, I do not think that young children - boys and girls - cannot like both "thing" based toys and "people" based toys. It has been found, on average, young girls are more attracted to "people" based toys and young boys are more attracted to "thing" based toys. Additionally, the empirical evidence that we have shows distinct differences between the transmission of neurotransmitters (serotonin and dopamine being the most obvious). These differences between hormones and neurotransmitters are biological (release of neurotransmitters can certainly be affected by neuroplasticity, but not so much so that the majority of women act in a way typically embodied by outliers). These differences are also maintained throughout life. (Differences in neurotransmitters can also effect the Big Five personality traits.) Just as older women and older men maintain the attraction to "people things" vs "object-based things." (Also cited in my article previously mentioned.)
It seems contradictory to believe a society that is created by men induces neuroplasticity in women and changes their personality so that the outcomes for women are better than men in so many areas: homelessness, suicide, and victims of violent crime are some of these areas.