Our late family dog, a Tibetan Spaniel, we got when he was about 5 years old was unneutered. He was a very loving and fun dog. Kept up with all of our play and the energy level of 3 growing children. He'd be a lap dog when we were still and he'd be playful when we wanted to play. He never sprayed or marked furniture or walls. When he had accidents in the house, it was just a pool on the floor since it never occurred to my parents to lay out pee pads. He was let out to go pee on his own a couple of times a day and also when he asks to go and did good.
He sometimes didn't lift his leg outside. He'd squat when he's feeling lazy or cold. And he never humped us or anything in the house. Can't speak for his manners outside when we're not looking. Somewhat opposite with our spayed shih-tzu. She'd sometimes lift her leg outside to go especially when there's a pile of snow out. She'd also give about 3 humps to our cat as a greeting everytime we return home from an outting which was, of course, daily.
Our female cat when she was spayed, did put on some weight as she was a slender girl for the most part, it was really noticeable. What they hollowed out of that lower part of her came back really sunken in, and eventually filled in with fat, etc., and kind of hung a little closer to the floor. Spaying did stop her from rolling around on the floor and "thrashing" because she was soooo needy. And it stopped her mating calls.