E brake is a replacement for conventional hand brake. Now its a button controlled electronically instead of physical pull cables.
Auto brake hold as explained above, keeps the car held in D without your foot physically in the brake pedal till you press the accelerator.
P mode in the gear box is parking mode of your car, but the biggest mistake people make in automatic cars is not use the parking brake thinking P will not allow the car to move. The fact is P locks the front wheels while parking brake locks the rear wheels. In P the locked front wheels are due to your gear box and without the parking brake the constant force and weight of the car is being put on the gearbox to keep it from moving.