Water pumps themselves never fail. A pump will always pump coolant unless there is no coolant in the tank or the V-belt is removed or broken. There are two real world ways in which water pumps do fail. They leak - usually from the small vent hole on the bottom, or the shaft bearing wears out. If your radiator is junk, upgrade your older BMW's radiator to an aluminum one. The price difference is small and the efficiency is much greater. On pre 1980 BMW's with M30 engines (or M20 320/6 or 323i models), use the post 1980 water pump as they are slightly larger.
Fan clutch failures almost only ever occur with the earliest six cylinder models, such as Bavaria, 3.0 CS, 3.0 CSi, 3.0 CSL, 530i etc. If there is resistance from the clutch when spinning the fan by hand, it's probably in good shape.
When bleeding the cooling system on M10 BMW's (2002, 2002tii, 320i, 320is, 318i etc), the system is self bleeding. But, you must take care to purge air pockets on six cylinder models any time you open up the system (ie remove the radiator cap).