Is it permissible for a wife to seek divorce or khul’ from her husband who is sexually deviant, does not fulfill her legitimate rights, and neither prays nor fasts, knowing that she has a child with him, and what are the implications of this regarding the custody of the son?

If the husband reaches such a level of evil as abandoning prayer and fasting, drinking alcohol, and engaging in sodomy, there is no good in remaining married to him. It is permissible for the wife to seek divorce from him, even through khul‘ (a type of divorce initiated by the wife by returning the dowry).

Custody belongs to the mother as long as she does not remarry. If she remarries, it transfers to whoever is most deserving of the females. Immorality is a disqualifying factor for custody, whether for the father or the mother.