Is it permissible, in Islamic law, to marry a second wife through a Fatiha recitation and witnesses, without an official marriage contract, knowing that the first wife has not yet agreed to this marriage?

If the woman is still married, it is not permissible for you to marry her, due to the Almighty's saying: "And all married women." However, if she has been divorced and her waiting period (iddah) has ended, then it is permissible to marry her with a valid Islamic contract that includes the permission of her guardian and the presence of witnesses. Documenting the contract in court is not a condition for the validity of the marriage, but it is preferable to do so to safeguard rights. The consent of the first wife is not a condition for the validity of marrying a second wife. It is obligatory for whoever marries more than one wife to be just between them in lodging and maintenance.