Is it permissible to take money from one's father with the intention that it is compensation for the effort of studying, and to spend it on basic needs, given that the father does not provide enough? And can it be given to the mother if it is unlawful?

Lying is forbidden and is a major sin. Its ugliness increases when it is done to parents. It is not permissible to take a person's money except with their permission and willing consent. Therefore, it is not permissible for you to take your father's money by deception, unless he has fallen short in providing the obligatory maintenance according to Islamic law. As for non-essential and recreational matters, it is not permissible to take from his money for them without his knowledge. You must repent and ask your father for forgiveness or return the money to him, even if indirectly. It is not permissible to give it to your mother because it is not yours. If your mother does not find maintenance, she may take from her husband's money what suffices her, in a reasonable manner, even without his knowledge.