For your final concern, if you have your bike upside down and turn the pedal once or twice to get the rear wheel spinning but then let it free-wheel, is that when you hear grinding and the pedals seem to move a little on their own?
If that’s the case I suppose it’s possible something happened in your rear hub. If it felt like the chain slipped or broke, but it didn’t actually move out of gear, then you might have your LBS look at it. Also with a brand new bike, it’s possible the cables will stretch under high load (shifting or mashing too hard in the wrong gear) causing the derailleurs to go out of adjustment (which is why good LBS offer free adjustments/tune ups).