Is the marriage of a previously married woman or a child in a third country without a guardian, with the presence of only one witness, without specifying the deferred mahr, and without completing the legal procedures, valid in Islamic law?

A valid marriage has pillars and conditions, including offer and acceptance between the woman's guardian (wali) or his representative, and the husband or his representative, and the presence of witnesses at the contract session. It is not a condition for it to be documented by the court; it is sufficient for it to fulfill the conditions of validity. It is not a condition to defer part of the mahr (dowry); it can be paid in full upfront, or deferred in full, or a combination of both. The guardian is required for a previously married woman (thayyib) just as for a virgin (bikr). The guardian can delegate another person to conduct the marriage, and the same conditions required for the guardian apply to the delegate.