Is it permissible to take money from one's father to cover study expenses or to establish a private business? Is it permissible to assist him in his work? What is the ruling on the income he earns from his work, considering that he previously worked in the tobacco industry, currently works in a stone quarry, evades taxes, pays bribes, does not pay zakat, and delays prayers beyond their prescribed times?

Your father's work in the stone quarry is permissible, and the money he earns from it is permissible. You are allowed to benefit from it and assist him in this work, as long as the work you engage in is permissible. As for bribery, delaying prayers, and not paying zakat, these are forbidden acts and major sins, but they do not render his work and money unlawful. Encourage your father in the good he has started doing, as that indicates remaining goodness within him.