Is it permissible for a son to help his father earn money, knowing that part of it will be used to buy cigarettes and another part for permissible things, and that the father has another source of income?

It is permissible to assist a parent in acquiring lawful money, even if he spends some of it on smoking, because it is an assistance in a permissible matter and not a direct assistance to smoking. The child should gently and courteously advise his father and forbid him from smoking.