Is the aforementioned agreement between the man and the woman considered a legitimate marriage contract in the Hanafi school, given the absence of a guardian and the non-existence of a dowry, and is the woman entitled to divorce herself based on the prior agreement, especially since the man refuses to divorce her?

The majority of scholars hold that a woman's marriage without a guardian is invalid, and this is the fatwa we adopt. This marriage is void, and the husband must divorce her. If he refuses, the judge should annul the marriage. This divorce is an irrevocable (bain) divorce. A woman does not have the right to divorce herself unless the husband, by his expression "You are free from this husband whenever you wish," intended to delegate this authority to her.

If the husband does not divorce her, and she is unable to obtain annulment from the judge, her recourse is to adopt the view of Imam Al-Shafi'i, which states that a فاسد (irregular/corrupt) marriage does not require a divorce or annulment to invalidate it.