All you need to order is a water pump seal kit (comes with a new shaft and 2 x seals), an oil filter and oil.
Replace these and tell the shop to leave everything else alone.
The only other thing you might need to replace is very possibly the spring for the bypass valve. But unlikely, do the filter and water pump seals first and then see.
I would tell the mechanics to leave everything else alone. If they don't listen take it off them.
Many people here have had the same symtoms, with the same fix.