Yours.
Not enough detail here to determine fault
it is the person coming out of the parking space
The vehicle exiting the parking space that did not yield to oncoming traffic.
It is your fault.
both of you for not looking back
My fault
Backing up--it is your fault.
I beleive, whoever's car is moving (wheel-wise), is at fault.
Depends on the jurisdiction, but typically, two vehicles backing up is a 50/50.
the person pulling out
The car pulling from the parking space is at fault