Is it possible to continue a marriage with a husband who searches for "maharem (incest), dayouth (cuckold), voyeurism" on Twitter, photographs his wife without her knowledge, publishes her pictures, then apologizes and claims repentance, knowing that he is negligent in prayer? And are these actions considered a fleeting indiscretion or a form of cuckoldry that has no cure?

Your husband lacks ghira (protective jealousy), commits forbidden acts, the worst of which is abandoning prayer, which leads him to commit every deviant behavior. We advise you to counsel him to repent, maintain prayers, avoid evil deeds, and associate with righteous people. There is no harm in referring him to a psychiatrist. If he repents and becomes upright, then stay with him. Otherwise, do not hesitate to separate from him, even through khul' (divorce initiated by the wife), because his companionship is a burden and corruption in both religious and worldly matters. Al-Mardawi holds the view that a woman can free herself from a husband who neglects the rights of Allah through khul' and similar means.