What is the ruling on one who curses religion when angered by something, and what is the duty of children towards him if he refuses advice, and what is the ruling on a marriage contract in which the father is the guardian while he curses religion?

Insulting the religion of Islam is disbelief (kufr), while insulting the religion of an inanimate object is abhorrent. You must advise your father gently and kindly to stop insulting religion. If he does not respond, there is no blame upon you. It is permissible for a father to appoint another person to finalize a contract, even if that person is a disbeliever.