Well if and when you get it started it belches black smoke the fuel is turned up to high on the adjustment screw on the backside of the right hand side of the fuel pump. Not being able to keep an Idle makes me think that too is messed up so I am willing to bet that someone "messed around" with the throttle arm, the idle adjustment and the fuel screw.
But all of those affect the running of the engine and not so much the starting. IF you are jumping to the glow plugs from the battery then you are getting around the circuit that normally makes that happen. But is the final result, making the plugs actually glow, actually happening? Pull each GP and jump it across the battery. Do not hold in your hand or place on anything that will melt. They glow red and will burn anything they are touching. I lay them on the metal shelf in front of the Radiator and hook jumpers on them their. If you have some that are damaged or broken apart, replace em, metal parts in the cylinder are not necessary to make the car run. You can test them for resistance in the engine block but you have to isolate them by taking off that copper strip that joins them all together.
Getting back to the hard start part. If the GP's are all good or new and it still does that hard start then I would be looking at the fuel delivery first and the compression in the cylinders second. If you are sure there is no air in the lines, verified with a clear hose at the inlet and outlets then the other possibility is that it just isn't developing the 480 PSI the engine needs to make the fuel go bang.
If you get it running again do you have a lot of smoke coming out of the vent tube that comes off the top of the engine? Or down low where the brake booster line goes in? Or do Jetta's not have that?
Those are the places I would look for what you are describing as a two fold problem. This is not a gasser so don't think the black smoke is too much choke on the engine when starting. The diesel is different in that way. There is no choke on the engine, just an advance timing control, Cold start it is called.