Were you both backing at the same time 'at impact'? Will depend on where damage is etc, but assuming both backing and bumpers hit more than likely will be a 50/50 liablitly decision made.
The person who is backing out of the parking space
both of you for not looking back
The person backing out due to the other car having the right-of-way.
Depends on the jurisdiction, but typically, two vehicles backing up is a 50/50.
the car backing out.
The person backing out I am asuming other person has finished reversing and is leaving if I understood correctly
You are. Improper backing.
Hard to say. Possibly equal fault by both parties but most likely the person backing out.
From the explanation given in the discussion area - it would unfortunately appear as if both drivers were at fault. The backing driver for not being aware of his surroundings, and the other driver for failing to yield to the backing car when he saw that the backing car was already in motion.
In most cases parking lots are private property and are not subject to street laws. Therefore, no insurance company will assume liability.
If he was driving forward past his intended parking space to take yours, then he is at fault. Cutting across is not permitted in parking lots although many people do it anyway.