Check engine oil that the water is entering into the sump from a blown headgasket.
Did you check to see if the fans are coming on. Wondering how you checked the water pump? It can only be checked for leaks or bad bearings which cause leaks in the seal. The coolant fans or the sensors that tell them to come on can caueit to over heat, a sticking thermostat can do it, blown head gasket, clogged radiator(flush it if it has a lot of miles) most likely the thermostat or the fans
Yes. If a water pump is leaking, it leaks anti freeze. Anti freeze, (coolant) can also leak from the radiator, or from water hoses.
Water pressure, how far the valve is open on the faucet probably should be looked at first. If the hoses are old, you might check for leaks.
check the heater core stopped up radiator
The radiator may be plugged. Take it to a radiator shop.
If your Whirlpool washer is leaking at water fill period, check to make sure that the hoses are tightly connected. They can sometimes loosen over time.
Check for water leaks in rubber hoses. Check radiator for leaks. Check for Low engine oil level. Check oil for water ingress (water droplets on dipstick) Check for water in cylinder (Check compression or remove spark plugs, check for rust or water spurring out hole when cranking engine).
If you had water in the cooling system and it froze, every component is a possible leak. Hoses, radiator, engine block itself.
check your coolent fill cap
Just plain evaporation.
It could just be that the water pump is not properly working. Have you checked all the could-be causes for your car overheating if not then do so.
you most likely need a new heater core or it maybe the heater hoses that go to it are leaking.