What is the ruling on one who abandons prayer out of laziness and negligence, and is he a disbeliever? And what must be done if the father does not pray, given the existence of fatwas that declare him a disbeliever, and others that do not? And is it permissible to adopt the majority opinion (fatwa) which does not declare him a disbeliever, after having heard previous fatwas that do declare him a disbeliever?

Your father is not considered an unbeliever by the majority of scholars. He is only deemed an unbeliever, according to the Hanbalis, if the Imam calls him to perform it and he refuses. One who abandons prayer commits a grave major sin, and you should continue to advise him. His guardianship for your marriage is valid and permissible according to the majority of scholars, who do not stipulate righteousness as a condition for the marriage guardian. There is no harm for you in following this opinion. In summary: your marriage is valid, and you should invite your father to prayer and explain the danger of abandoning it.