Is a girl considered legally married if her guardian agrees in front of witnesses, and she agrees, and the Fatiha is recited, and her Mahr is paid to her secretly? And do her family have the right to annul this marriage without the consent of the husband or the wife?

If marriage is agreed upon without the conclusion of a legal (Shar'i) contract, the girl is not considered your wife, even if you have paid part of the dowry. This is because the marriage contract is valid only upon fulfilling its legal (Shar'i) conditions. Reciting Al-Fatiha at the time of engagement or contract has no legal basis. What occurred between you is merely a legal engagement, which is a non-binding contract for both parties, and either party has the right to annul it. However, it should be fulfilled religiously if there is no legal reason for annulment. If the girl does not consent to the annulment, her guardian is not permitted to annul the engagement and prevent her from marrying if the suitor is suitable, and the girl has the right to resort to the religious court. In the event of annulment by the woman or her guardian, she must return to you what you provided to her as dowry and gifts, and you have the right to claim that through legal proceedings.