What is the ruling on a father who commands lying and bearing false witness to obtain money, claiming that it is permissible, and is he considered a disbeliever? And does our father's payment of Zakat suffice for us, especially since I have a university stipend that is not enough to cover basic needs, and my sister has a dowry that is only spent on marriage matters?

If the state provides a sum of money to those who have no one to support them, and your father is supporting you, then it is not permissible for you to take the money, or to commit fraud and lie. Nor is it permissible for your father to seek to obtain the money through deceit and fraud, and he should be advised with wisdom. Your maintenance is obligatory upon your father, unless you are married or possess sufficient wealth for life's necessities. Zakat is only obligatory when the nisab is met and a full year has passed over it. It is permissible for your father to pay Zakat on your behalf with your permission.