Is it permissible to postpone the payment of zakat debt owed by the deceased, or to give it to needy relatives, or to spend it on an ongoing charity (Sadaqah Jariyah)?

If the father did not leave behind an inheritance sufficient to cover his debt, then his children are not religiously obligated to pay off the debt, whether he made a will to that effect or not. This is a religious ruling, not a discouragement; rather, it is commendable to pay it off because it is a form of birr (filial piety/righteousness). If it becomes clear that repayment is not obligatory, then it is permissible to delay it. If the money allocated for debt repayment is zakat money, then the entity that managed the father's business must be informed that it is zakat money, or it should be spent on the eight categories of zakat recipients if that is not possible, as ongoing charity (sadaqa jariya) is not one of the zakat categories. If the uncle or his children are among the zakat recipients, it is permissible to give them the amount, but the father's will to equip the uncle's children is not obligatory to fulfill.