a knackered water pump normally shows as overheating when at speed,the pump impeller does not spin at the same speed as the shaft, around town at low revs it genreally stays within the correct temps. A faulty water pump will not cause coolant loss unless it has boiled up out of the expansion tank and you would see that.
Is there signs of a leak anywhere or has the car running issues that may point to head gasket failure?
Although the rad may look OK, most of the corrosion happens in the area you cannot see, like under the fan, have really good look and take the fan off if you can. I would be suprised if the rad isin good shape after 10 years, but then UK uses loads of roadsalt, does NZ too?