Are all the aforementioned divorces valid, and what is the ruling on the first divorce, and is the marriage contract annulled by her divorce if he does not take her back, believing that it did not occur?

First divorce pronouncement: If it was a mere thought, nothing is entailed. If it was a promissory statement like "I will divorce her," then no divorce occurs.

Second divorce pronouncement: A husband divorcing his wife during menstruation or during a period of purity in which he had intercourse with her, is considered valid according to the most preponderant and authoritative opinion, which is that of the majority of jurists. If it was with an explicit verbalization, or an implicit statement accompanied by the intention to effect a divorce, then the divorce has occurred.

Third divorce pronouncement: Divorce by writing does not occur unless accompanied by intention.

Revocable divorce: If the husband divorces his wife with the first or second pronouncement, the divorce is revocable, and he has the right to take her back as long as she is within her waiting period ('iddah).