When EV mode is applied, it will run the car off all-electric power alone, the ICE wont even turn, but if your in "regular" mode the car can be driven up to 42-50mph on just battery power, but the ICE will spin, but use no gasoline, and you will still get 100+mpg.
I always just power down instead of hitting "P". Otherwise I would never get any sleep because I would be worried that I left the car on. When I turn the car on in the morning, it is in P. I only use the emergency brake if I am on any sort of incline. I have not had an issue.
2. EV mode is handy if you are only 'starting' the car to move it around the driveway to let someone else's car out. No need to warm up the ICE for a 25 foot trip.