Hi Shawn,
Answer to your Question #1:
Yes, Magnetic Calibration (MagCal Algorithm) run automatically and continuously as long as the Demo is running. When you run the Demo for the first time, there will be a Magnet Icon below Start Button indicating calibration is pending. After you Hit start button calibration starts and you should now rotate the Board across all AXIS or figure of 8 to enable the algorithm to acquire diverse samples and get an acceptable degree of Hard and Soft Iron calibration.
Answer to your Question #2:
The Demo employs Hard as well as Soft iron Calibration which is applicable for eCompass (FXOS8700).
Please refer to Application Note AN4246 for details.