I have a 2013 Range Rover Autobiography, even if l have been on a long journey so that the battery should be fully charged l still get a message to start the engine as the battery is low.

Hello, sounds like a problem with the battery. Have the battery tested for charge and the ability to handle a load. It could be getting weak, and seeming less capable to the vehicle's electronics to be able to function appropriately. Not sure what to say about the door; perhaps it needs to be checked for proper operation.