Water pump pulley shakes during rotation

The bearing on front of water pump is probably shot. I've seen a few times where water pump did not leak from weep hole, or did not have one when the bearing was worn. This would cause the "wobble" or vibration of the pulley. Replace the pump.

At this point I would be concerned that the engines head gasket has taken some damage. The faulty water pump may have been the initial cause of overheating, but if the head or head gasket are now damaged, the added pressure in the system could have caused the radiator to fail. You can try replacing just the water pump and radiator (and do a new thermostat as well) but be prepared ... and keep a very close eye on your fluid condition and level (both coolant and oil) and engine temps for the next month or so. If there is still a problem you'll most likely need to repair the engine - sorry.