Are a second divorce and an oral reconciliation valid, and if not, what should the woman do? And does the waiting period (iddah) count from the second or third divorce, in the event that her husband divorced her orally, then took her back before the end of the waiting period, then officially divorced her with a divorce document, then took her back without obtaining a marriage document, then divorced her orally?

Formal documentation of a divorce is not a prerequisite; once it occurs, it is valid. If a man divorces his wife with three pronouncements, she becomes irrevocably separated from him (baynunah kubra) and is not permissible for him again until she marries another husband, consummates the marriage with him, he divorces her, and her waiting period (iddah (definition)) from him ends. This is based on the Almighty's saying: "And if he has divorced her [for the third time], then she is not lawful to him afterward until she marries another husband. And if he divorces her [afterward], there is no blame upon them for returning to each other" (Quran 2:230). This applies if the husband had taken back his wife after the second divorce before her waiting period expired. However, if no reconciliation occurred until the waiting period from the second divorce ended, she becomes irrevocably separated from him, and his third divorce pronouncement does not affect her. He is then permitted to marry her with a new contract. Reconciliation (ruju') does not require documentation or a new contract. If reconciliation occurs between two divorce pronouncements, the waiting period is calculated from the third pronouncement. However, if no reconciliation occurs until the waiting period from the second divorce has ended, the waiting period is not calculated from the third pronouncement because it did not take effect on her.