If you ask them for the OBD codes they should know what you are referencing but a lot of shops unknowingly use a standard OBD tester you need one that can read Mercedes OBD codes.
They should give them to you you paid for the diagnostics.
Drivers back light as in the break light, or blinker light, or reverse light?
I'm sure some others will chime in on this. To me you seem to have two different problems and I still don't believe its the BCM and don't want you to waste your money.