Is an informal marriage (zawaj urfi) that took place without a guardian (wali) or the audible pronouncement of the marriage formula (sighat al-aqd) valid, and does a woman's subsequent marriage to another man make her married to two men if the first marriage was not dissolved?

If the marriage contract was concluded without a guardian (wali), and sufficed with writing the formula and the signatures of witnesses without uttering the offer (ījāb) and acceptance (qabūl), then the contract is invalid, even according to the Hanafis. It is not concluded by writing between those who are present. Consequently, this invalid contract does not require divorce or annulment. If the second marriage fulfills its legitimate conditions and pillars, then it is valid, and you are under the marital protection of the second husband.