Is a customary marriage between a Shiite woman and a Sunni man valid and permissible in Islamic law, and what is the procedure to be followed in the event of divorce in such a marriage?

If the conditions for the validity of marriage are met in an urfi (customary) marriage, then it is valid; otherwise, it is not. There is no requirement for witnesses for divorce. So, when a man pronounces a divorce, it takes effect even if there are no witnesses. Witnessing is only recommended, based on the Almighty’s saying: "And call to witness two just persons from among you." It is not a condition that it be in a documented contract.