Only the passenger side mirror is supposed to move down when reversing. This is acting properly.
For the light that you are seeing, this is normal as well. Its called a cornering light and only works on Auto mode. It is not always on. When you corner, your low beam lights turn in the direction you are turning. Well this means they are not pointing straight anymore. So the cornering light illuminates to fill that void while the low beams turn in the direction you are turning. After you straighten the wheel this light stays on for a little then will fade away. You will notice this if you pull up behind a car after cornerning you will see only one light on. If the wheel is straight it will fade, or if you turn the wheel again. Completely normal, nothing wrong at all