I think the fan noise is just from being old and a little loose I know mine sometimes makes noise so if i hit the dash hard enough it shuts up
As far as buying from the stealership goes...did you check online, parts stores, and junk yards first?
The radiator cap holds 13lbs of pressure in the system to keep everything flowing properly. If its rusted or worn out, it doesn't do its job and the liquid doesn't flow properly. Of course, a bad radiator cap usually, not all the time, causes overheating.
Also, what does your temp gauge read at?
I'd do a coolant flush and replace the thermostat first for sure.