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2012 Hyundai Sonata "shift to park" indicator

The indicator next to my speedometer read “Shift to Park”. I let off the brake the car went move back until I hear click and it stop moving but the auxiliary items were still on. The car beeped when the key was away from the vehicle and the remote key was unable to lock the car.

Firmly apply the parking brake before shifting to park, then the car will not move and you will not hear the pawl clicking.
On many vehicles auxiliary items remain on until you open the door.
As far as the electrical problem, unlikely powertrain warranty will cover that. So, your choice a good independent shop or a Hyundai service department, expect to pay $100-150 for diagnosis.