That does sound too hot, my 300D (with a new radiator stays between 85-95C in 90-100F temperatures with the AC running. It will only reach 100+C if I climb a very long steep hill at highway speeds, then it cools down immediately on the downhill drive.

I don't know what the "tiny pieces of orange" are but it does sound like you need a cooling system flush. You may also have some air trapped in the system. Some times disconnecting the upper radiator hose and filling through there helps. Also, try running the heat for a little while to remove any air from the heater core. It will probably be easier to flush it first, them worry about the air when you refill the system. Don't worry about the "extra" gasket, it's probably for another application. If none of this helps, you can try reinstalling the old thermostat.