Hi there. Perhaps I can help.
Backfires are the product of lean conditions. As backfires occur, several sensors will send out signals that are out of range and the on-board computer will react by setting error codes that pertain to those signals. That means that a backfire caused by insufficient fuel pressure might result in MAF, O2 and misfire codes.
We're dealing here with a very sophiscated fuel delivery system that includes a fuel pump that has a three-phase motor, which ensures sufficient torque across the whole pump speed range. The pump speed is used to provide the required fuel pressure of 3-6 bar (43-87 psi), depending on the engine operating state.
A fuel pressure sensor sends its signal to the MSS60. The fuel pressure sensor is located behind the inner fenderwell. If the pressure sensor fails or there is a fault in the CAN bus and in the engine emergency program, the fuel pump is operated at full speed. In this process, the pressure is limited to 6 bar by the mechanical pressure sensor.
The signals from both tank fill level sensors are sent to the junction box and are forwarded to the instrument cluster via the K-CAN, where they are evaluated and displayed.
This is going to be hard to diagnose without access to ISTA software; measuring fuel pressure would confirm insufficient fuel as the cause of the backfires, but won't tell us whether it is caused by a false reading from the fuel pressure sensor, or a weak fuel pump, or bad wiring, or even a bad computer.
If you don't have ISTA, you might consider taking the vehicle somewhere where they do and can pinpoint the problem as a cheaper option to what is happening now.
Please let me know if you have any other questions.