Is it permissible for a woman to seek divorce from her husband who insists on committing sins and neglects prayer, and did the Prophet, may Allah’s prayers and peace be upon him, rule for divorce in such a case, especially with her fear of him deviating further after the divorce?

If a husband neglects prayer and commits evil deeds, and the wife has made every effort to reform him without success, then it is permissible for her to seek a divorce from him. In fact, it is preferable, as Ibn Muflih mentioned that a woman may seek khul' if her husband abandons a right due to Allah.