Is a deferred dower and wife’s maintenance payable after her insistence on divorce and initiating khulʿ? And what is the father's right to custody should he move to an Islamic country?

If a wife is divorced, she is entitled to her deferred mahr (dowry), and this right is not forfeited unless there is an agreement to divorce in exchange for it. Her merely asking for divorce does not forfeit it.

A disobedient (nashiz) wife forfeits her right to maintenance during the period of her disobedience, unless she is pregnant, according to the Maliki school and one narration from the Hanbali school.

The maintenance of children is obligatory upon the father as long as they are young and have no wealth. As for the custody of children, it is a right for the mother as long as she does not remarry, and it may transfer to the father under certain conditions.