Am I obligated to give money to my father, who asks for money but does not spend it on his family, and who has lied to me before, claiming the money was for household expenses while he was consuming qat? And does the saying of the Prophet, peace and blessings be upon him, "You and your wealth belong to your father," apply to my situation?

It is permissible for a father to take from his son's wealth if he is in need, provided that it does not harm the son and that he does not take it to give to another sibling. The majority of scholars have restricted this to necessity, based on the Prophet's (peace be upon him) saying: "You and your wealth belong to your father." It is not permissible to give money to the father if he will use it to buy something forbidden, such as "qat," due to the implication of aiding in sin. However, if he is in need of support and it is possible that he might buy qat with part of the money, he should be given what he needs without harming the son, while advising him to abandon what is forbidden. It is preferable to directly purchase the family's needs if possible, along with showing dutifulness to the father and advising him not to spend on disobeying Allah.