Allroad 2.5 Tdi: How do I know if my water pump broke?

Hello.

I have a 2005 Audi Allroad 2.5 Tdi which is overheating when I climb hills or accelerate much. On idle it stays at 90 degrees, and if I drive it smoothly in the city (not too many hills) it will take some time before it rises. I changed the thermostat and had some sort of "external" wash to the radiator although (didn't see how it was done, but the mechanic said pressurized water is directed to the radiator to remove dirt). This apparently helped a little bit but the mechanic says the radiator has to be pulled off and cleaned internally. I haven't found anything saying aluminum radiators need to be cleaned internally, but before they remove the radiator I will try a radiator cleaner from Liqui Moly hoping that if there really is something clogging it, this will unclog it. But being realistic, I don't think this will solve my problem, and would like to know how to determine if the water pump is failing? I read on another page that changing the thermostat involves almost the same work as changing the water pump and timing belt since they are all in the same area. When the mechanic changed the thermostats, would he then have been able to see the water pump's impeller to determine if it was good or damaged? Has anyone had to clean their alluminum radiator?

Thanks from Guatemala...