Serious mechanics with serious feedback?

I will be as detailed as possible. Ok my fiancee juss got a 97 Chevy Camaro 6 cyl frm a family friend of hers. She hasn't paid anything yet BUT I think the car has been sitting prior to her recieving it for some time. She had been having issues with her car putting and then stopping when she is at a quarter tank of gas. It would always crank up but randomly put and try to stop. We recently found out she needed a new radiator because the old one was really rusted out. The car ran hot and we had it changed but the thermostat kept saying it was running hot but when you go under the hood there's no sign of overheating. No smoke, no sizzle, no burning smell, etc. So feed bakc kept saying it was the thermostat and I had a problem with mine before and figured it was too plus it was recommended to change the cooling switch so she had it all changed by a friend who is a mechanic. Once he put everything on and we checked it...the thermostat was still reading hot and still no smoke or anything under the hood. The friend said its seems like the water pump because the top radiator hose you detach to replace the thermostat which the water goes thru feels like its pulsing when it should have a smooth flow going thru. He said it may have been the problem. I would like different opinions cuz my gf is kinda stressin. Plus when she is driving you can feel the car kinda drive funny like it doesnt wanna take off. Is the water pump and what is your personal advice for what it seems like the problem is. if you need more detail...will provide