Is it permissible to kill a father who used to pray then stopped, based on fatwas that allow the killing of one who abandons prayer if he does not repent?

You must advise your father to pray and not despair of his guidance, using various methods and seeking help from those your father respects. No one has the right to implement the hudud punishments, including the hadd for abandoning prayer, except the ruler or his deputy, such as a judge; this is because the enforcement of hudud falls under the authority of the Imam (leader).