What is the ruling regarding a wife staying with her husband who does not pray, does not fast, and asks her to engage in anal sex, and is it permissible for her to seek a divorce?

The crime of abandoning prayer and fasting is greater than any other crime after associating partners with Allah. Therefore, you must advise your husband to pray and fast. It is not permissible for you to obey him in what he asks of you regarding anal intercourse, for there is no obedience to a creature in disobedience to the Creator. Rather, it is a grave sin, and a curse has been reported against its perpetrator, and that Allah will not look at him. If your husband repents, then praise be to Allah. If he insists, then seek a divorce. If he refuses, then raise the matter with the Sharia courts.