If you back into a car you are At Fault, especially if the other vehicle was parked. You are the one with the responsibility to look behind you and to avoid the accident. If both cars are moving all bets are off.
The car in the back is usually at fault in a rear end collision. The only exception would be if the car in front were backing up. The car in back is at fault for hitting you ,but if you are pushed into the car in front of you you are at fault for hitting that car.
the car that back into the other car
The person's who parked it there, (its parked illegally.)Not your fault.
If car A is in front of car B, then car A is at fault
As far as I understand, if any car is in reverse it is their fault.
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
The backing car 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.
the car who bumped into you
The fault of the one who backed in to you, unless you made a very unpredictable, unnecessary stop.