[wiswind]

The thing about fuel pressure / delivery, there will be NO CEL to tell you about it.
There is NO sensor for fuel flow or pressure.
There have been a few posts where people had fuel delivery issues, but backfiring was not mentioned in any of them.
The best way to troubleshoot the fuel system is to connect a fuel pressure gauge to the test point on the fuel rail.
A good shop will have a isolator......which will isolate the gauge from the fuel.
This would enable them to use a long line to the gauge.....and be able to take the vehicle for a drive, while monitoring the fuel pressure at the fuel rail.
Not having the isolator would make this a unsafe practice.

A good shop will also have the equipment to connect up and monitor various engine functions......and know how to interpret them.
There are OBDII monitoring programs that you run on your laptop computer.....but those also require one to be able to interpret the data that you see.
A good diagnostic can save you money over guessing.....and a lot of frustration.

I would certainly get the battery checked out to make sure that it is not contributing to your issues.
I would expect the battery voltage to be pretty constant over various RPMs.....once it is charged up.

A starter relay could contribute to starter problems.....but not to the driveability problems.

A fuel pump relay is a higher failure item....but again....it would be throwing a part at the vehicle...
Spark plug wires and (in my opinion if still original) a coil pack are tune-up items ....that are good to do at this point anyhow.
Another good to do would be to replace the fuel filter, air filter and clean the MAF with MAF cleaner that you can buy at most auto part stores.