water pump question 4.6 HSE

hi everyone, im having a few intermittent overheating problems, hot water overflow at header tank, i will be changing thermostat & header tank cap next week, and was thinking of putting a new water pump on just incase.
Just wondered though, as my heater is working correctly can i presume that the water pump is doing its job.
Could somebody also let me know the correct procedure for re filling the system with coolant, to avoid air blocks etc

Thanks you

check the rad for cold spots.