IMO a dog of age two is usually still evolving in his mind. I consider all dogs as puppies under the age of three. Why you might ask? Experience. A lot of dogs will only start to show behaviours at age two and a half to three. I consider these behaviours to be true adult behaviours and not a puppy going through hormone changes. If a puppy at 18 months starts to exhibit strange behaviours, I put it down to going through puberty and trying to push buttons. After three, puberty is in the past and the true behaviour is now evident. Unless marked intervention at this point, I always find that the behaviour will escalate.
That being said, I have never had a dog change his disposition, unless a medical issue is evident after being neutered when older. I have neutered older than 9 and the only thing that changed was his desire to wander and they tend to get a bit lazier because the hormones are not urging him to find what is missing in his life. (A lady love)
As Debra said, I would consider the peeing in the hallway a learned behaviour at this point. He has probably gotten away with it and in my experience, dogs do what they are successful at. If he gets away with it, he will try it again, and again, and again, until he is no longer successful. Something like counter surfing. Shadow used to get away with it and will still eye the counter, but since he can't get away with it anymore (the duh person that used to leave food on the counter now puts it away after having his sandwich stolen, it only took about 4 years to get that one!) he doesn't try to get on the counter anymore.
Personally, I would neuter him if you are not planning to use him in a breeding program. I find them more prone to being calmer and more biddable (not by much as this is a B after all!) than if you leave him intact. Also, if you are not using him in a breeding program, this will put your mind at ease that this is definitely not a sexual experience for him. It definitely sounds like excitement over dominance as well. I have one girl, who will be spayed soon, that tends to get nippy with the other dogs and nasty when her prey drive escalates. That is when she HAS to go into a crate to settle down. She gets a chewy or toy in the crate and stays in for about a 15 min timeout to settle herself. I will expect her to settle down better after she is spayed. I may have her bred once more, but that will be it. Why have her get that upset if it isn't doing anything for her?
Just MO of course.