Answer your first question first, yes, they will. My dog has 8 brothers and sisters. He plays particularly well with one of them...even they have not seen each other for mths, the moment they get together, they just GEL. And you can tell they know each other's limit. They will take turn to be the down one during wrestling. Both are not neutered yet. When dogs not agree with each other, they have their own way to settle things, that's why in nature, there is a leader and there are the followers.
You watch, very soon....you will have few responses telling you that
you need to neuter your dog, if not, you will contribute to the large population of shelter dogs. I get their points but this is another view.
I have no objection on neutering but to me it's about the timing and the training you are willing to put in. Sometimes people neuter their dogs because they only got one side of view (from vet, etc) or they don't want to deal with the potential (potential, not WILL BE) issues.
If you read any animal physiology textbook, you will find out the importance of testosterone towards muscle and skeletal growth. And male's growth plate takes longer to close. If you neuter your dog too early, he won't have the hormone to grow properly...not all dogs will have problems...but without the proper physical development, the dog could get injure easier.
Obviously with the hormone, you can be sure you will get a "sometimes rebellious" teenager....but from my own experience, with the proper training and socialization, it's NOT HARD to control. But not everybody is willing to give the time. Some people think that well the unneutered dogs will make other dogs pregnant...ok, this happens because of irresponsible owners....Come on, no responsible dog owners will let their dogs run free and have a sex party.
I think neutering needs to be done, because not so much about your dog attacks other, it's more about other dogs attack your dog when they smell the testosterone. So in order to have a peaceful time at dog park, eventually, that's the way to go. So if I were you, I would wait till your dog reaches physical maturity and top health, then do it.
BTW, I know people said Non-neutered dogs are aggressive, not necessary...I saw more aggressive neutered dogs in the dog park. Pretty much all the dogs I know that are non-neutered are perfect gentlemen. So I think the aggressiveness is more about the up bringing of the dog than the chemical...