If I recall in the application there's a feature to export a txt file description, or some such. (However, personally, I just use X-Plane for buttons and axes, as I find the configurable app to be terrible to use.)
Good question. Not sure you can. But maybe a question for the authors on the Aerosoft forum.
Depressing the buttons should make them appear in white in the X-Plane joystick configuration window. You may have to scroll up and down to find them.
I suggest doing any controls configuration or troubleshooting while the aircraft is loaded (use non-persistent mode or a fresh airframe).
P.S. Also to not that with the ProDeskSim each lever only supports one physical button, either ATS disconnect or TOGA (the other isn't even wired up).