Sounds like your problem is lurking in the wiring.
Consider paying for an hour or 2 with a good mobile auto electrician, they can usually get to the bottom of the problem.
If you ask them to delete the aftermarket immobiliser, you should still have the ECU immobiliser.
I think you are correct, the fault will have been generated by connecting the battery without the air bag connected.
The air bag fault is one of the safety items, along with ABS, that stays on even if the fault is fixed.
Not all fault code readers can clear those faults, the only sure way of sorting as Hardmonkeys said is vagcom
-The auto electrician my have a good enough reader or vagcom itself.