Is it permissible for a wife to abandon her husband who insults her family, utters obscene words, confessed to her that he committed adultery before marriage, and neither prays nor fasts? And what is the permissible duration of abandonment?

This man is evil because he abandons prayer and fasting, has bad manners, and lacks modesty. There is no good in remaining with him. The sister should advise him, and if he responds, then that is well and good. Otherwise, she should take her case to court to separate them.