First things first....yes yes yes you want it registered either as an RV or a private bus. Some guys are getting better insurance rates on a private bus, but I'm not sure if you would given your age. There are also other benefits to being registered as an RV, but we don't need to go into that until you figure out if you have a choice in the first place. Again, what my agent told me is that the rates for RV's are NOT based on the age of the operator.
The 392 is a GREAT engine. Just make sure you find out the gear ratio of the rear and and if it has a governor. I can't imagine you want a bus that will only do 45. Part of having a skoolie is the journey, but 45 mph on the interstate might make things a bit too scenic.
You were correct in assuming that hydraulic brakes are like on a car. These use a pressurized fluid to move the shoes into contact with the drums. The difference, however, might come in the power assist system. While some buses with hydraulic brakes have a booster that uses engine vacuum to assist much like a car, it seems that far more have a hydraboost system instead. In this system, pressure from the power steering pump (which is essentially just a hydraulic pump ) is routed to a booster which then provides the vacuum assist. 1 ton pickups have had this system for YEARS and it tends to be very reliable.
Air brakes are kind of a different animal. I will go ahead and put my neck on the line in saying they stop better. This is the same system 18 wheelers and trains use, afterall. With air brakes, an air compressor on the engine will pump a set of air tanks under the chassis up to about 120 psi. When you step on the brake pedal (called a treadle in air brake applications), an amount of air is routed to the brakes. It is proportionate to how hard you push the pedal. Push harder and you put more pressure to the brakes. At the wheels themselves there will be chambers. Inside these are pistons which when pushed will move the shoes into contact with the drums. Additionally, your parking brakes will be air operated. The shoes in this system are held against the drums by heavy springs. When you push the release lever, air is applied against these springs causing them to retract. That means that you must have air pressure to start moving and if you lose air pressure on the road, the brakes will automatically come on.
I don't want to complicate things and admittedly I am not the best at describing these things with words so I'll let someone else try.
Do make sure you read the air brake section of the CDL regulations. There are some important numbers to know and braking techniques to understand. I certainly hope I'm not scaring you away from them! They are a fantastic braking system. You just need to fully understand them. It does give you an air supply for running air tools, an air ride seat, BIG air horns....whatever you want!
If you choose to go with the Chevy buses, rest assured that the 366 is also a popular gasser motor and another well built piece. I *think* Chevy was actually the last company to offer a gas engine in a bus and it was the 366 with throttle body fuel injection.
As for convincing your parents....it might be hard at first, but after you buy it, make sure you make progress on it, but take your time. Make it look nice. Do a good job on the electrical and plumbing systems. Take shortcuts within what's safe to fit your budget, but don't let them know
I'm sure they will come around. Just make sure you keep up on it. There are all too many half finished skoolie projects on eBay because people lose interest.
If your parents are anything like mine, and I bet they are, they will come around as they see it come together. My parents scoffed at the idea, but once they saw exactly what it was, they started to like it a little. Maybe you just need to take them camping once. They'll never go back.
Best of luck and keep us posted.