Is it permissible for me to take spending money from my father who works in a usurious bank, and is my grandmother among those whom I am obligated to support and is it permissible for me to take the money she gifts to me, knowing that she receives a pension from a previous job in a usurious bank?

Working in a usurious bank is forbidden (haram), and the money earned from it is unlawful (haram). Benefiting from this money is a matter of dispute among scholars: some believe it is forbidden to benefit from it except in cases of necessity or poverty, and one should only take what is essential. Others believe that money that is unlawful due to its earning is only forbidden for the earner, and it is permissible for others to benefit from it. The first opinion is more cautious. This applies to your grandmother's money as well. As for your grandmother spending on you, it is not obligatory while your father is alive, as the financial responsibility lies with the father.