In short, during the normal combustion process, there is always some air/fuel charge that escapes past the rings into the crankcase. The pcv valve is in place to ventilate or evacuate the crankcase of this unwanted pressure and for emissions purpose to reburn the air/fuel charge
I suppose so. I doubt it's the pump though. Unless you have suffered from the highly unlikely probability that the water pump impeller has brken from the shaft in which I think you would hear noise. Thermostat is easy quick and easy to change.
You have described what sounds like a thermostat issue. It is stuck closed or only partially open. Usuaually a bad water pump will just leak from the shaft seal if bad