Is it permissible for a son to take from his father's money without his knowledge? Is that considered theft? And is the opposite permissible?

It is not permissible for a son to take from his father's money without his permission; otherwise, it would be considered theft. However, if the father does not provide his son with his essential maintenance, and the father is capable, while the son is in need and unable to earn a living, then the son may take what is sufficient for him in a reasonable manner. The proof for this is the narration of Hind bint Utbah, when the Prophet, peace and blessings be upon him, said to her: "Take what is sufficient for you and your child in a reasonable manner."