1985 Pontiac Fiero trying to read codes from diagnostic gm

The SES (Service Engine Soon) light may be burned out. The light should illuminate when you first turn the ign. On, if not the bulb may be burned out.
When you are in the diagnostic mode the ECM will take all computer advance (timing) out, so the engine will idle at 500rpm (vs normal 900). Also is diagnostic mode the SES light will blink every second.
You can remove the IP cover with a torx screwdriver and reach behind it to replace the bulb.

If the bulb is working when ign. Is on you may not be grounding A and B terminals of the ALDL. These are the only two terminals together or next to each other.

Backfiring is could be timing, fuel or camshaft timing gears.

Check fuel pressure with a mechanical gauge (should be 13psi on a TBI engine).
Remove distributor cap, rotate engine (clockwise then counterclockwise) with ratchet on balancer pully looking at dist. Rotor for degrees of play in timing gears.
These cars are know to fry ignition modules due to heat issues (not a lot of airflow in a mid-engine car).

If the SES light works and you ground terminals A&B of the ALDL, the SES light (ign on not running) should flash code 12 three times, then any error codes three times. When all error codes are displayed it will flash code 12 again.

I would check fuel pressure first, should be 13 psi on the TBI engine. IF OK:

Check spark using a spark plug tool where you connect the plug wire to the tool, ground it to the block, crank the engine looking for spark. If OK

Remove the cap and rotate engine in both directions looking for degrees of play in timing gears.

My guess would be if everything is OK the ignition module is fryed.

IF the ECM will not display codes (12) then the ECM could be bad.

You have to isolate one problem at a time, fuel, spark.

If you suspect a FP relay you can run 12V from the cigarette lighter to terminal "G" of the ALDL. This will run the pump all the time, bypassing the relay.
This car is equipped with a backup FP pressure system. Where if the FP relay fails and oil pressure (while cranking) is above 7psi, the oil pump circuit will power the pump.