What is the ruling on a customary ('urfi) marriage without a guardian, with reference to the Hanafi school? And what is the solution if the husband refuses to register the divorce or to pay the deferred dower?

The majority of scholars consider marriage without a guardian (wali) to be invalid, but it is valid according to Abu Hanifa. A customary marriage (نكاح عرفي) is valid for those who believe in its validity, following Abu Hanifa, or by a ruling from a شرعي judge, provided there are two witnesses and a dower (mahr). The husband has the right to divorce without requiring witnesses, and the wife is entitled to the dower, both deferred and prompt, upon consummation, even if the marriage is invalid. She can bring the matter before a judge with documents proving her right, and the husband is not permitted to destroy them.