He should be neutered....but peeing all over the place. you need to limit his area in the house. He has too much free space if he is not asking for the door.
I limit Pixie to the living room, kitchen, bathroom basically I shut the bedroom doors. I keep a pee pad in the bathroom for her to use. She usually asks for the door. She also uses her pee pad. If Pixie is active she pees every 2 to 4 hrs.
I would start limiting his space and start over with the house breaking and take him out every 2 hrs and praise him when he goes and use one word that describes going to the bathroom...out.... pee pee....what ever you are going to use and always say that word when asking to go out and when praising. hope this helps