<<They are distortions because a person reading it comes away with the impression that men are everything in Yiddishkeit and women are second place, merely yentas,servants or property etc >>
Careful now not to bring it the other way. That’s not acceptable either. As to your points:
We don’t learn to daven from Chana. We learn to daven outloud from her. The Avos set up the davening and much of the siddur is from Dovid. The Amidah is from the Anshe Keneset HaGadol.
The merit of the women is one of the reasons we were redeemed from Egypt. The Midrash lists many others including the suffering of the children who the Egyptians buried alive in stone walls, to not changing our language and dress, etc. They are all reasons for the redemption says the parush marazo
The men failed by chet hagel because the men fly higher than the women. If you fly high you can fall. So you also have to credit the men for taking us on a higher journey, for setting up the Torah and Jewish life to the extent Hashem grants us that power. This is why Rav Hirsch says men as zachar, are the zicharon, the carriers of the tradition. I could argue that the women didn’t sin because they were sitting around talking. I wouldn’t say that about the great women of that generation but you get the point, falling has to be understood in context.
Women were spoken to first at har Sinai but the man was spoken to first in gad eden. the Maharal says in gad eden only one mitzvah was given and since women are less spiritual Chava was less able to handle it and you see she initiated the first sin. At har sinai a full system was being given so you could approach the women first and needed to to enforce in them the idea of the importance of Torah. Tiferes Israel 28
According to the Netziv, only Sarah’s ruach hakodesh was higher and that’s because she was in the tent and Avraham was exposed to the masses. But avraham’s navuah was higher. Rav A. Miller says the same and that of course Avraham was her rebbe. R’ Soloveitchik says the matter is limited to certain matters of social, familial relationships.
Bottom line is you are dealing with two types of spirituality. The woman has more of an emunah peshuta that works somewhat intuitively and has a certain stability to it. The man has more of a high flying spirituality (has more chochos hanefesh says the maharal) and can crash because of this but without him you don’t go on much of a journey. You need both types of people.