Does Islamic Sharia approve of a girl marrying a young man who stipulated that she quit her studies and work, especially since schooling in her country is only in mixed-sex schools?

If the young man proposing has religiosity, good character, and competence, then his conditions indicate his piety and zeal, and he should not be rejected because of them. Mixed-gender education and a woman's going out expose her to corruption. The man does not object to a woman's acquiring knowledge or working, but he wants this to be within her home. This is a good matter through which a woman can acquire knowledge via open education, external enrollment, or legitimate scholarly programs, while safeguarding herself from mixing with men.