CS, basically none of the chasidishe schools teach more than Chumash with Rashi, with lots of other seforim for mussar. Some chassidishe schools, including satmar, do not teach with Rashi, because that’s considered torah sheball peh according to them.
The litvishe are very maikil and will teach tons of meforshim on tanach, but will never teach mishnayos and gemara(except pirkei avos). They hold that anything used to understand torah she’biksav isn’t an issue.
The vast majority of ehrliche women throughout history were completely uneducated in seforim. According to you, did they all indulge in goyishe things? Chas veshalom! A girl who grows up knowing what their purpose is and who is taught the dangers of goyishe culture will not get involved in such things, whether they’re chasidishe or litvishe.
But some girls simply don’t keep what they’re taught. And if you want to start getting into anecdotal incidents…. those with glass houses shouldn’t throw stones. Have you seen what became accepted in crown heights in recent years? Are you aware of how many girls – and boys – who can rattle off sichos but are engaged in kol minei nivalah?
A woman’s ruchnius isn’t from learning. It’s from tznius, chesed and davening. Learning Torah accomplishes everything for a man; it does very little for women. Perhaps it can be an element of avodad Hashem, but there’s a reason why it is not a chiyuv – and we know that גדול המצווה ועושה, one who does what he is obligated to do is bigger than one who does something they’re not obligated to do. It’s a basic chazal; the enthusiasm women might have over learning could be the same kind of yatzer hora that makes men more interested in chessed than learning – it’s a yatzer hora.