I know I have two stage heat because of the aux. heat option. But how do I determine whether I have two stage cooling?

If you have auxiliary heat, you have a heat pump. In would be very unlikely that you had a heat pump with two stage cooling... but anything is possible. Pull the cover off your themostat and see what is connected. And you could always search the model number online for a description and possibly an owners manual for your unit. Good luck.