Do you see the open gap at the top of the "after" pictures. Notice how at corner the gap closes, but on both sides of it, the gap is open?
I believe that gap is showing me the internals of the pump. AKA that gap is not supposed to be there and beyond being totally screwed up, is not allowing the pump to develop suction. Sort of like how an engine can't develop compression if there is a large hole in the combustion chamber.
I don't think there is any pressure transfer through the pump sections. That gap shouldn't make a difference. There's a shaft in there that turns the piggy backed pumps, but it should have a seal. I think the tram pump should still work even if the two PTO pumps sections were removed. I could be mistaken, though.
As for a charge pump...
That's internal to the tram pump and not visible.
The tram pump in neutral just spins and doesn't move any fluid, because the swash plate is in a neutral position. When you push the treadle pedal, it changes the angle of the swash plate. The more positive the angle the faster you go in one direction. The more negative the angle, the faster you go in the other direction. It forces fluid through the wheel motors. So that's kind of a closed loop. But some oil slips past seals and case drains, etc. and goes back to the tank. The charge pump makes up that lost oil, and maintains a base pressure on the tram pump, as I understand it.
Also, the hydraulic filter only filters any fluid that the charge pump sucks in to the tram pump (suction filter). It doesn't filter any fluid in the PTO pumps that are constantly pumping. They have a separate intake(s) from the tank than the tram pump.
I'd guess when you install a new tram pump, you'd have to fill the unit with oil manually, then perform the bleed procedure until no air comes through the bleed hose back into the tank. If you're still getting air bubbles after several total minutes of bleeding, there's a couple reasons that I can think of.
Very low level in the hydraulic tank.
Filter not sealed to the filter housing.
Pump wasn't filled with fluid before attempting the bleed and doesn't have enough fluid in it to start suction.
If you're getting not oil coming out of the bleed hose, don't run the engine until you can get the bleed hose to pump out only oil into the tank by just cranking the starter in 10-15 second bursts (to keep from overheating the starter) with the spark plugs removed so the engine doesn't fire.