Is a wife's refusal to engage in marital intimacy with her husband, due to his repeated and harmful violence, considered a sin? And is she permitted to seek divorce for harm (طلاق للضرر) in this situation?

A wife sins if she disobeys her husband regarding his request for intimacy. If she is harmed by the method of intercourse, she must be frank with him and guide him to the appropriate method. If he responds, she is not permitted to refuse. If he does not respond, she is not disobedient for not complying, because "there should be no harm nor reciprocating harm." As for seeking divorce for the aforementioned reason, the general rule is that it is not permissible unless she is harmed by remaining married, due to the Prophet's (peace be upon him) saying: "Any woman who asks her husband for divorce without any strong reason, the scent of Paradise will be forbidden to her."