Does divorce occur during menstruation? Is it considered adultery? Is it permissible to marry another man with the intention of returning to the first husband?

As long as you have asked people of knowledge whose religiosity and scholarship are trusted, and they have issued a fatwa to you that the bid‘i divorce (innovated divorce) did not occur, and you have acted upon their fatwa, then there is no blame upon you. For whoever imitates a scholar in a disputed matter and acts according to his opinion, then his obligation has been fulfilled, and he is not allowed to revert from this fatwa in the same incident.

Therefore, there is no blame upon you for remaining under the marital bond of your husband, and there is no need for separation, nor for resorting to "tahlil" (halala marriage), as it is a false and forbidden stratagem.