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His...obviously
The driver who is backing up. That person has created a traffic hazard/impediment and is totally responsible.
It is the fault of the person backing out. You have the right-of-way if you are driving in a usual and safe manor. The person who hit you should be cited for "backing without caution".
if you're reversing into your driveway and someone hits you its their fault. you were moving away and they wern't paying attention. Now if you went back into the street to straighten out and back back in then it might be your fault, but if you were reversing the whole way and never came back out of your driveway it would be theirs
if the car b pulls in out of no where and with out the signal is car b fault
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.
the car who bumped into you
Answering "Pulling out of a parking lot onto a street and you have to back up to avoid on coming car and the car behind you hits you who is at fault?"
If one of you broke, then it would be the one who didn't break who would be at fault, if neither of you broke you are both at fault for undue care and attention.
This can go either way, most often it is the person who was backing out that is at fault. witnesses would be great to prove this is what happened.
The general rule of thumb is that any car moving that hits a parked car is at fault.
Not enough detail here to determine fault