Do not get your dog neutered it will not help with aggression problems, it will only make your vet money. Do not go to a positive-only trainer, positive-only training is the biggest con in dog training there is, there are four quadrants to dog training that make up the whole of the pie, positive reinforcement, negative reinforcement, positive punishment and negative punishment, to have a well balanced, reliable and obedient dog you must use all four quadrants. The fact of the matter is 95% of dog owners and the wider public, in general, do not know how to train dogs, they do not have obedient dogs and if you ask anyone they will have their own theories on how a dog should be trained, but often tout old wives tales that simply do not work and are outright dangerous, the positive only movement whilst well-intentioned has only served to create millions of unsafe poorly trained dogs, led by companies like PETA who have a vast amount of money and play on peoples emotions instead of observable fact. But, alas I won't spend all night going on about positive-only reinforcement issues and instead will answer your questions as best I can.
1, Your dog by your own words is very spoilt, this is a major problem with dog owners, a dog should not be babied, and certainly, a big guardian breed like yours, what you describe in your post is a dog who has no respect for his owner or the rules of our society, this is a structure and training issue, your dog simply hasn't been told what it can and can not do, you need to be a confident k9 leader and teach the dog how to behave like a well mannered k9 citizen. I advise you to find a high level "balanced" trainer who uses all four quadrants of dog training and specialises in problem dogs ( dogs with aggression issues, dogs with these issues can not be fixed with positive-only reinforcement). The reason your dog will listen in the house and not outside of it is because he has no compulsion to listen to you outside of it, your dog blocking your path when other people are around or acting aggressively towards strangers is caused by him sensing a threat and not feeling confident in you as his owner handling the situation so reacts with aggression, quite simply he does not view you as a leader so has taken a proactive role in deciding who is a threat and how to handle it.
2, do not let strangers touch your dog, contrary to popular belief dogs do not like being touched by strangers and this is a perfectly normal thing, it is incredibly uncommon for a dog to love social interaction with every stranger they meet, now of course this is a generalisation as there are exceptions to every rule.
3. in the case of your vet, your dog should be muzzled at all times when visiting the vets now that he has displayed this behaviour, you should take him on regular visits with the same vet so he can become used to that particular vet, its important to note that although this can be done over time with specific people, such as family who will see the dog regularly or your vet, dogs don't generalise well so you cant condition a dog to like everybody it's simply not possible, but with your vet, you can certainly teach your dog to tolerate handling by them, by using positive reinforcement to reward positive social interaction with your vet, and correcting any aggressive behaviours(don't try this without first being shown how to do so correctly by an experienced professional)
4, keep your dog away from dog parks this is a recipe for disaster, dog parks are some of the worst places you can take your dog and sooner or later it always ends up in a dog fight and potentially a human getting bit breaking up a dog fight, the majority of the dog-owning world do not have control over there dogs.
5, Take a look at Leerburg for some great tutorials on establishing pack structure, teaching your dog behaviours with positive reinforcement and marker training and the use of corrections in training, Michael Ellis is widely thought of as one of the best if not the best dog trainers in the world has a great free video on youtube on his philosophy of dog training.
6, Shield k9, has tons of free videos that show you how to train a fully functional offlead obedient dog, if you are great at self-teaching you can pick up a lot of info from these videos, they also have paid courses an elite off-leash obedience course and a puppy elite course, as well as reactive rehab course that goes hand in hand with their elite off-leash course, I highly recommend their system of training, if you follow their steps you can have a completely obedient off-leash dog in 6 weeks, I now walk all my dogs off-leash everywhere they go and one had a lot of reactive aggression issues.
Here is a list of top trainers you can find on youtube that will really expand your mind when it comes to functional dog training that actually works, Shield k9 (Haz), Michael Ellis, Ed Frawley, Tom Davis (upstate canine academy), Nate Schoemer to name just a few.
The bottom line, is your dog needs proper training and structure get experienced help if you need it don't go looking for a quick fix like neutering which will just waste your money and not solve any aggression issues, it's important to remember most vets are not dog trainers and have very little experience in training dogs to any decent level, the same goes for behaviourists who often lack experience actually handling dogs, instead find your self a trainer who works and fixes(ask for proof) aggressive dog behaviours regularly.
I hope this helps, if you have any more specific questions on training or would like me to direct you to videos just ask.