Is a husband permitted to prevent his wife from seeking knowledge if that leads to her neglecting her household duties, and is she obligated to fulfill household responsibilities such as cooking, tidying, and raising children with the husband's help if he is able?

A husband can prevent his wife from going out to study, unless the knowledge is an individual obligation (fardh al-ayn) for her, such as learning the rules of prayer. In that case, he must provide a means for her to learn; otherwise, she is permitted to go out to seek that obligatory knowledge, even without his permission. Learning individual obligations takes precedence over raising children and household chores. It is not permissible for a husband to prevent her from learning what she needs concerning the rulings of menstruation (haydh), postpartum bleeding (nifas), and irregular bleeding (istihada); rather, he must teach her or allow her to go out to inquire.