“That is why women have more health problems than men”
This is a highly dubious statement; in almost every country, women are longer-lived than men.
“He says that women don’t wear tzitzis because the inyan of tzitzis is very deep”
Halachically, women can wear tzitzit. Why women have taken on some mitzvot for which they are patur such as shofar, but not others such as tzitzit, requires further research.
“Men are definitely more intellectual than women – as a whole.”
That may no longer be the case; women now outnumber men in all levels of higher education enrollment.
“I once commented in real life that women shouldn’t be judges, because hormonal fluctuations can affect a person’s perception of the case.”
It doesn’t seem to have hurt Ruth Bader Ginsburg, Sonia Sotomayor, or Elana Kagan. They may all be postmenopausal, though. In any case, in a universally accepted tshuvah, Rav Uziel z’tz’l pointed out that a woman CAN be a Dayan on a beit din for a property dispute as long as both parties to the case accept here. That has not happened since no woman has earned yadin yadin semichah but it might at some point in the future.
“The Ralbag was not trying to degrade women, he was writing for men.”
All the rishonim were writing for men, as women didn’t have opportunity to learn Torah back then. Baruch HaShem that has changed! In any case, medieval Christian and Muslim attitudes towards women were far more negative.