What is the religious ruling on helping the mother financially, or by buying a commodity for her, or on the wife paying off the mother’s debt from her own money—whether saved or not—after the husband swore, "Divorce be upon me if you sell your gold, I will not give you a single dinar"?

It is not permissible to swear by other than Allah, and the prohibition is intensified if it is by divorce (talaq). The one who swore must repent and seek forgiveness. As for the ruling on the oath, if it is a conditional divorce, it takes effect as soon as the condition is met. The oath is specified and restricted by the intention of the swearer. So, if he intended that the money from the sale of gold should not reach his mother, then the divorce takes effect if that occurs. But if he intended something specific, it does not take effect unless what he specifically intended occurs. As for doubt about the wording of the divorce or its number, what is certain is the lesser amount, and the ruling on the marriage does not change except with certainty. It is best to refer issues of divorce and swearing by it to Sharia courts or to consult scholars directly.