I think you have some great replies but I wanted to perhaps point out a few things I noticed that were "missed" or different from my opinion.
#1 The link between neutering and aggression is not a firm scientific link. It is based on statistical data with inconsistent control factors. So neutering may not tone down the aggression. What neutering will do is prevent the poor dog from suffering from "roaming" issues when a female dog is in heat and it will significantly reduce the occurrance of cancer, which is very probable. The odds of a dog developing cancer grow exponentially the longer they are intact, especially if the breeding program was less than stellar.
#2 Behavior and behavioral tendencies are genetic to some degree. Again we are going back to the breeding program. Since it is unlikely to know what that program was or who the parents are, then temperament issues are going to be a bit harder to diagnose. I really don't agree that there are no bad dogs just bad owners. Quite frankly that isn't true, cause I am a very good owner and my dog has very severe food aggression issues, while I may have provided the right environment for them to flourish, she had to have an innate tendency towards this time of aggression for it to come out as it does. So yes environment plays some role but so does genetics.
#3 Dominance displays that are as blatant as you describe are a very clear and concise way are to be taken VERY seriously. I can guarantee you, if you had called our rescue about a dog with behavioral issues like you describe, we would not have taken the dog, and if we had to, we would euthanize the dog ourselves. That being said, we are a rescue with different responsibilities than an owner, we just don't have the resources or the liability to take on such a dog. But, I personally feel that independent owners should do what is necessary to ensure the safety of both their dog and the general public.
Ok, my recommendation, get your friend the information on NILF method. This will help her gain control of the "pack" without putting herself at risk. I also strongly recommend that you implement the program too, start with your own dog so that you are in the habit of the method when you babysit the dog. This way your uncertainty wont be challenged by him. You and your friend are at a point where "Tough love" is necessary to ensure the safety of all. Then you need to get a trainer/behavioral consultant IMMEDIATELY. they will have more tools to help you work with this boy to help him become more stable and you to be more confident in your leadership. Also I would recommend contacting a local pit bull rescue, not to rehome, but to get some advice from people who are used to working with unstable and untrained dogs of the same breed. They may have some tips and tools as well. I work as the owner surrender and training coordinator for my rescue, and my job is to help owners like your friend get the information they need so that any "permanent" decisions (rehoming or euthanization) are made with complete knowledge of the tasks at hand.
Trust is a tricky thing, once lost it is very hard to gain back and unfortunately that is when the dog suffers most.
I have to say though, you both are very courageous to step up and ask for help. Many let these things slide until there is no more choices available. With the right training method and behavioral plan, this dog can become a valued member of the family and a great friend to all. I will admit it is going to take work, and lots of it, but if you and her are committed to making it happen, then you have a chance to rehabilitate the dog and gain that trust back.