Is it permissible to give Zakat al-Mal (obligatory charity on wealth) to the mother to pay off her debt, or to the student sister who does not have enough to suffice her, or to the brother whose income is insufficient, knowing that the father has a pension that is not enough for the family and that the son lives with them when he returns?

A Muslim is not permitted to give his Zakat (definition) to his parents for their sustenance because they are already his responsibility to support. However, it is permissible to pay off their debts from Zakat if they are in debt and do not possess the means to repay it. As for the sister, it is permissible to use Zakat for her study expenses under certain conditions. And as for the brother, it is permissible to give him Zakat if his income is insufficient for his basic needs, as this is both charity and maintaining kinship ties.