just remove the readiator cap and rev the engine. you can see the water flowing when the engine is at operating temperature already. pag malamig pa engine di mo makikita na nag-flow yung water kasi close pa ang thermostats.

as per replacing the water pump, remove the fan belts then you'll need 10mm wrench to remove the pulley and 12mm wrench to remove the pump. some also have circlips on the shaft but you can remove this with a screw driver and a lot of patience (not to mention dexterity). make sure you clean out all the gaskets from the block before you install the replacement water pump or else it will leak from the gasket.