Hi,

No one has suggested this but I would clean the throttle body.
The FPR has it’s on port and is on the side so it’s not so influenced by the plate so much but senes the overall flow through the intake.

Check the two ports up on top to be clear of gunk all the way through and the surfaces below them are clean at the top of the throttle plate.
Make hoses are not leaking, especially all the way down to the vapor evaporation canister.
Sometimes that valve on it needs cleaning too in case it’s stuck open.

Make sure that the plate closes all the way shut at the bottom tightly.
Check the throttle plate to barely wiggle open and that the throttle switch click when the motion is seen but not to have it open hardly any at all.

The plate and switch creates a transition period and the computer needs a heads up that it’s about to change flow but really hasn’t started by much.
If this system gets out of adjustment the transition is not smooth.

It doesn’t get out of adjustment easily unless neglected fir a long time or someone tries to tweak the idle speed by playing with the stop screw on the left.
The IAC and the throttle switch have to do it all.

If the car was stalling, it is saying one thing and that’s too lean or too much air.
If it’s that the AMM doesn’t know about and so does the ECU!
The backfiring is the same thing.
This is when, I also get suspicious of a loose clamp or crack in the accordion tube behind the AMM.

Until you get all of these possibilities check off, as good, don’t go blaming a AMM.
You want that to be the last item to do a test replacement with! As there’s no testing it.
Only make sure all the pins are clean and engaging across the group inside the connector.

Good luck looking.
There are others that can help you sift through this stuff, as it’s a common thing, that many times does fall under some simple maintenance care.

Phil