Is it permissible for a teacher to give private lessons to the son of someone whose money he knows is unlawful, and is it permissible to take payment from him?

If all the guardian's money is unlawful, then it is not permissible to take a wage from him. If his money is mixed, it is not permissible to take a wage from the unlawful money itself. However, if the wage is from money other than the unlawful money itself, then that is disliked (makruh) and not prohibited (haram) according to the majority of scholars.