No power starts fine, has no power and has gradually got worse. Now only just moves. The black pump think next to fuel pump - you can keep pumping but it doesn't harden even when engine is not running. There are air bubbles in fuel pipe.

This could be due to a fuel system problem, perhaps a clogged fuel filter. Since any debris in your gas tank would be settled to the bottom for the initial startup, the fuel pump picks up clean gas and has no problem supplying the injectors. As you drive, the circulation of the gas from the tank through the filter could cause the filter to plug up with debris, gradually losing power until fuel pressure is not sufficient to keep the car running. Try replacing the fuel filter and running some fuel injector cleaner through with your next fill-up.

There is a fuel pump prime cycle (2 or 3 seconds)when you turn the key to on and once you start the engine the fuel pump power comes though the oil pressure switch.No oil pressure,no power to the pump.maybe your oil pressure switch has become weak?I would use a scan tool and command the fuel pump on when it does shut off,just to make sure the pump can run,as it could be a bad pump too.Also when it does quit,if you turn the key off for 10 seconds, you should get a prime cycle by turning the key to on.Have someone listen at the gas tank for a fuel pump noise,which will be only 2 or 3 seconds,but will do as a pump running check.Next would be to check for power at the back at or near the fuel pump,power and no pump.replace pump.No power to pump,follow power back to the front through oil pressure switch and fuel pump relay etc.You can always add your own power to the pump from a power source the switches off with the key if needed bypassing the existing wiring and oil pressure switch.

It should be four wires. Gray is power to the pump, Purple is gauge control, and two black wires that are ground. You should have battery voltage on the gray for 3 sec. after the key is turned on. Did you replace the plug-in to the pump when you replaced the pump? The pumps usually come with new plugs

If the battery is strong and charged, starter is fine, car ran okay while getting progressively worse until it died and won't restart now, might be fuel filter or pump. I've dealt with two cars with fuel filter issues. Both would idle fine, but run progessively worse under load and eventually die and not start although everything else checked out. Engine turned fast enought to start, battery strong, alternator fine, air cleaner clean, all that. No start. Changed fuel filters and done. Everything back to normal. Both cars were about model year 1990 (1989 and 1991). Replaced one in a parking lot and car fired right back up and powered on home just fine, whereas the week leading up to it it ran worse and worse, hesitated on acceleration and finally would die if you hit the gas. Fuel filter may be in engine compartment. Looks like a canister with an in and an out for fuel. Pump is in gas tank and is way more work and money. Good luck, hope this helps.

check your fuel pressure, also check to see if there is a booster pump, some ford rangers have a booster pump inline... fuel injected units need to have at least 35-45 psi some even higher around 50 psi...

Your problem is the fuel pump pressure check valve is defective, this is part of the fuel pump and the fuel pump is located in the fuel tank. Have the fuel pump replaced.

Fuel pump is overheating (means it is failing) replace it.

TRY ANOTHER FUEL PUMP AND FUEL FILTHER THESE PUMPS ARE FUNNY ON VOLVOS HAD SAME PROBLEM ON 850 TURBO AND SURE ENOUGG IT WAS THE PUMP

Have you check the transmission fluid level? It sounds like it is low. You might not have a dipstick in that unit. I'd add at least 2 quarts and test drive it. 

sounds like you have a huge vacuum leak at the engine, check under the hood for a sucking noise, I think you will find one.