Something is wrong with my cat, please help?

I have a maine coon cat who will be turning 13 on July. He is constantly licking himself, which ends up making his fur all nasty and it is also making him have hairballs constantly. Not only is he having hairballs he is also vomiting up his food about once a week. He likes to stay in the hottest room in the house, which is probably 90 degrees right now. And we can't get him to stop going up there, because the door doesn't close all the way. Also where ever he is when he hears either the sink or the bathtub water running he will run to them just to drink water when he has water in his bowl. It doesn't make sense. This past week he has also been meowing almost constantly. Please help me, my asshole dad doesn't think anything is really wrong with him so he wont bring him to the vet and my mom doesn't want to go against my dad...I am really worried because this is my cat and I dont want him to die on me!