Ok, this is going to hurt - a lot - but you need to hear it.
First off, with all the time and money you spent on this, you would have been much better off taking a freshman physics class - and an English class - at your local community college. Your utterly basic misunderstanding about "gravity" being a type of energy is easily solved in the first few weeks of a freshman physics course --- as long as you are willing to listen/learn. That's a big open question here, though, because based on your responses so far, it doesn't sound like you have any interest whatsoever in learning. You have your ideas about how the universe
should work and are utterly uninterested in how it
does work. Ordinarily, that's harmless, but in this case, you've spent time and money developing something that is just complete nonsense. And now that it has a patent, I suspect you are going to waste more time and money trying to sell the idea. Thats a lot of damage to you (not to mention to the integrity of patents) and that's the reason I'm still working on this rather than just deleting the thread.
Anyway, a good intro physics course always includes a few sample problems relating gravitational potential energy and kinetic energy of a dropped object, which shows how the energy is conserved. It also shows - using the definition of work - why there is no energy input required for a table to support a book, which is an obvious way of illustrating that "gravity" is not an energy source.
In the description of Machine #1, you talk about momentum. Momentum and energy are two different things and momentum is irrelevant here. The weight of the device itself is also irrelevant: when you lower it and raise it, the GPE is the same and no energy is gained or lost. For the actual function, though, we have to change the idea a little bit because the way it is described, it won't even be able to stop sinking. Water is very viscous and dense and you are going to lose most of your GPE to hydrodynamic drag. You dismissed that with a hand-wave, but you really can't - presumably you've been in a pool at least once in your life, so you should already know that when an object is dropped, it falls to the bottom very slowly. So we'll need to change this device to one that captures and stores the GPE as it falls, reducing the loss to drag. The actual mechanism for capturing the energy is irrelevant and there are a lot of ways to do it. What is important is that we assume
all of the GPE can be captured while it is falling.
So let's throw some numbers at it and see what we can get. Let's say you have a 10kg mass device of arbitrarily small volume (so virtually no buoyancy itself). If you lower the object 10m into the water, you recover E=mgh=10*9.8*10=980J of energy. Now you use that energy to pump out the water/create a void. Again, the mechanism is irrelevant: the pumping energy is just E=pv. The pressure is p=rho*g*h where rho is the density of water (1000 kg/m^3).
So you have 980J=(1000*9.8*10)v...or v= .01m^3
Now remembering that your object is 10kg, this .01M^3 tank has a net buoyancy of (1000*.01-10)*9.8 = 0
So as you can see, the theoretical maximum performance of such a device isn't that it will come back to the surface, but rather that it only can generate enough energy with the fall to give itself enough buoyancy to halt its own fall. Now since it is at this point neutrally buoyant, you could always raise it back up to the surface with almost no input of energy and restart the process...if your machine is efficient, you haven't lost much energy, but clearly you haven't gained anything.
This analysis forms the foundation of all buoyancy motors and is the sort of analysis a freshman physics prof might put in the first test as an extra credit problem (prove that this PMM works/doesn't work...). If that sounds condescending, it is meant to: you need to start accepting that the concepts you are dealing with here are so simple that you should
learn them instead of spending years ignoring them while wasting your time on a hundreds of years old failed PMM idea.
The analysis of the other buoyancy motors you "invented" works pretty much the same way. I'll get into some more specifics later (thread remains locked for now).
BTW, I couldn't view the photos on the USPTO's viewer, so if anyone else is having similar problems, here's a pdf:
http://www.freepatentsonline.com/7770389.pdf