Must I fast what I vowed to the woman who claimed she would break the spell, and if so, for how long must I fast? And what is the solution if I am bewitched while my family is not convinced of the matter?

What the woman mentioned is a form of fortune-telling and claiming knowledge of the unseen. It is not permissible to believe her or to base rulings on her words, due to the Prophet, peace and blessings be upon him, saying: "Whoever comes to a fortuneteller or soothsayer and believes what he says, has disbelieved in what was revealed to Muhammad, peace and blessings be upon him." It is not permissible to go to her even to ask, for "whoever comes to a soothsayer and asks him about something, his prayer will not be accepted for forty days."

Her knowledge of individuals' names might be through deception or through jinn, and delayed marriage does not necessarily mean the presence of magic. If the existence of magic is proven, it has a cure.

As for fasting, it is not obligatory, because the vow is contingent on something that has not materialized and is uncertain.