What is the ruling on an unregistered marriage to a second wife, with two witnesses, when she is divorced and has children, out of fear of committing adultery, and the wife is aware of the Shar'i ruling? And is this marriage considered void if laws prohibit polygamy, with an agreement not to have children using contraceptives?

If the 'Urfi marriage fulfills the conditions of a valid marriage (offer, acceptance, guardian, and witnesses), then it is valid. If a condition is missing, such as the absence of a guardian, then it is invalid according to the majority of jurists, unless the contract is concluded in imitation of the Madhhab of Abu Hanifa, in which case it is valid. It is permissible for the spouses to agree to temporarily postpone procreation when there is a need, using easy and less harmful methods. Islamic law has permitted polygyny for those who are able to be just, and a law that contradicts the law of Allah has no value.