I use Moto Body because Google Fit can be disabled while Moto Body measuring cannot be disabled, so this saves battery, I suppose.
Steps are quite accurate, and heart rate too, when it gets a reading. Distance is not.
YES you can with the 'tasker' and 'Security settings' apps.
See "Auto enable expanded desktop" on xda-developers.com.
You'll need to add both an 'Enter' and an 'exit' action.