I have no leaking from the water pump - and the heater works well.
I'd take that as a positive, if the heater is working then I'd be 99% convinced the water pump was doing it's job as well. The feed/returns for the heater are only 1/2" pipes and so I'd be very surprised if that would operate by thermosyphon alone, I think given the layout it will need some pressure from the pump.
I did notice that the rad is very slow to heat up and the top hose next the the thermostat housing is way hotter than the hose at the front of the engine.
Is there a way to test my water pump is operating correctly
Now I haven't tested mine, but I'd expect the top hose to be significantly hotter than the one into the front cover plate, that should be the return from the radiator. I would expect to feel a notable difference between the top and bottom hoses of the radiator as well.
As for testing the pump I think that's a bit more complex. I can think of checking the drive belt is good and turning the pump with no slippage, but after that I'm not sure of any definitive tests you could do easily. It's a simple design and if it's not leaking then the only way it can't work is if the impeller has broken up (noisy, wouldn't turn) or is slipping on the shaft. That actually happened on mine, but it was my first replacement pump and with hindsight it did press onto the shaft with little pressure; we put it down to not being machined correctly because the second one was much tighter and is still there today. I can't imagine that's the problem with yours.
Perhaps with the thermostat removed and the radiator cap off the header tank you might see some level movement if you flicked the engine from tickover to say 3,000rpm rapidly ? I'm clutching at straws really.
My thoughts are with BDA, check the instruments. I'd put a meter between the regulator and gauge to see if it's getting 10v or 12v. Incidentally, is the fuel gauge about right or is that also reading higher than expected ? (same feed)
As for the sender, it's easy to see if one has failed completely because it will have virtually zero resistance & go directly to earth/full scale deflection on the gauge. One that's partially failed is harder to spot without checking the resistance vs temperature. There's also a chance you have the wrong sender for the gauge, I think they do come in different resistances ?