Is it permissible for the wife to return to the husband after she requested a divorce via text message, and he responded with another message saying, "You are divorced," and then he took her back by saying, "I have taken you back into my عصمة (bond of marriage) and you have one divorce (remaining)" after a valid private meeting, especially since she was menstruating at the time of the divorce?

The divorce initiated by the husband over the phone takes effect if he intended it. If the divorce occurs before consummation but after a valid private seclusion (khalwa shar'iyya), the re-marriage (raj'a) is valid according to the Hanbalis without a new contract, though it is preferable to renew the contract out of consideration for the opinion of the majority. The presence of menstruation does not prevent the occurrence of divorce, whether before or after consummation, according to the majority of scholars. Divorce issued by the husband is binding and does not require witnesses, with the caveat that it is impermissible to request a divorce without a valid Shar'i reason.