I think your water pump would either leak or make nasty noises. I can't think of a realistic way for it to stop pumping. If it's shaft broke you'd throw your timing belt & you would probably notice that...

T-stat or radiator should make your engine run too hot. How does your temperature gauge run?

A blown headgasket can make bubbles in your coolant. A leakdown test can check that.

Make sure the radiator cap and the hose going to the reservoir are OK. As the engine cools down, it's supposed to suck coolant back into the radiator. If the hose leaks then it sucks air instead of coolant. Those are easy to check before you go looking for exotic problems.