For those who have looked to AFG with hope of seeing stability & especially progress on human rights, this news (combined with the closure of secondary schools for girls & young women, isn't at all welcome.
From: https://www.khaama.com/talibans-latest-statement-necessitates-women-to-wear-burqa-in-public87539/
"At a press conference in Kabul, a spokesman...read a statement.... ...if a woman did not cover her face outside the home, her father or closest male relative would be summoned and eventually incarcerated or fired from government jobs."
As for the witness, I've heard that in some situations, witness of two women is equal to witness of one man. In some situations, witness of a woman is unacceptable. And finally in some other situations, witness of men and women are equal. Regarding the #hadith you cited about "deficiency" of women's mind, the hadiths correctness is unknown.
Regarding the verse from 3:34, strike them does not necessary mean physically. And if it is done physically, it must be light and not hurting the face or gentials. Right now, I don't remember where the hadithes were for this. Also read footnote for this verse in quran.com:
Note that I'm not sure what the footnote says is wrong or not. Regarding the exceptions of strike, I know that from the punishment for some other crimes that it is forbidden to strike on face or on gential. Also fire as punishment or to kill is forbidden according to a hadith.
That is what I know and in general, I don't know much about Hadiths, only #quran