Is the husband entitled to reclaim the dowry (mahr) and gold if he has not consummated the marriage with his wife, who returned to her family's home after one month? Does she have to observe an 'iddah (waiting period)? What is the ruling on this case regarding whether it is a khul' (divorce at the wife's instance, with compensation) or a talaq (unilateral divorce by the husband)? And is she permitted to become engaged to another man?

If the wife stayed with her husband for approximately a month and there was privacy between them, and the husband was an adult and not castrated, then she is entitled to the Mahr (dowry), and she is obligated to observe the 'Iddah (waiting period). It is not permissible to explicitly propose to her during the 'Iddah, but it is permissible to allude to it. If an agreement is reached to return the Mahr or something similar to the husband in exchange for divorce, then this is Khul' (divorce at the wife's instance by giving compensation), and it is permissible for the husband to take it.