I took out thermostat in a pot filled it with water brought it to a boil it didnt open

I ran my car without it it overheated. I put a new radiator new clutch fan thermostat new belts and coolant I let in warm up took the cap off the radiator was full but the water was backing up not circulating meaning my water pump is going out not working proper no signs of water in oil creamy color or coming out of tailpipe I revved up the motor noticed the fan wasn't spinning as fast as it should the water pump and fan share the same pulley its internal did not see any see page from where the bearing sits on housing my question is I implemented all other possibilities its not a blown head gasket,

I narrowed it down to the water pump the hoses are secure and all tight no leaks do I have to change the timing belt if I change the water pump? For removal what gaskets seals will need to be replaced I have a 4 cyl& The water pump and timing belt are side by side internally what parts are removed external the pulleys the cover plate that sits under the pulley. Does the head assembly need to be removed to access the water pump &timing belt should I do a compression check make sure the valves or ok check if I have cracks in the cylinder blocks or head