Is it permissible for the heirs to waive the debt for the son and daughters only, to the exclusion of the husband, given that the deceased also has other debts and obligatory Zakat that he did not pay, and how should the inheritance be distributed in this case?

First, the debts of the deceased, including the obligatory Zakat, must be paid before the inheritance is divided, according to the verse: (from after any legacy which he may have bequeathed or a debt). If someone, being a mature and رشيد (of sound judgment) adult, waives their debt, this is a valid waiver and is considered a gift. If the debt is waived only for the sons and daughters, it should be divided equally among them. If the deceased woman left no heirs except for the husband, two sons, and daughters, then the husband receives one-fourth due to the presence of a lineal descendant, and the remainder is for the sons and daughters by virtue of 'asabah, with the male receiving the share of two females.