That's an OBDII system. The light will not go off until you have a mechanic use a scanner to reset the ECM. Autozone and Advance do not reset the ECM, as they are not supposed to. Most of their scan tools are not capable.
Only a real shop can reset it. Unhooking the battery will not clear the codes on an OBDII system. That information is not necessarily for you Hawklore, just general information in light of someone suggesting you disconnect the battery.
I hate anything Ford computerized, their system just plain sucks. The newer is not so bad as the older stuff, but it still sucks.
Check to see if the backfire caused it to blow a gasket or seal anywhere in the exhaust. If it did, it can pick up fresh air in the exhaust and read lean.
Check the fuel filter to see if it is clogged. You can also look at the general state of tune, plugs, wires, cap, rotor, filter etc. I doubt you can move the timing. Tap on the mass air flow sensor, if applicable, and look for wiring problems with the sensor connectors. If you find none of the above (and really look, test, and try, if this is an intermittent problem you'll have to work at it) then have them hook a scan tool to it and see if the O2 sensor is switching like it should. if it is not, replace it. With a genuine OEM sensor and not some cheap crap from Autozone or Advance. Only genuine OEM tune up parts or sensors should be used on late model vehicles, there's too much crap floating around in the aftermarket pretending to be good parts.
By the way, the only reason to step on the gas when trying to start a vehicle with electronic fuel injection is the extremely rare case of possible flooding, which is next to impossible to do with EFI. All stepping on the gas does is SHUT OFF the fuel.
If they put an IAC motor on it, and did not properly reset the base idle, the idle air counts, and the minimum air rate, it will not start good, and it will not maintain an idle speed. It may die, stall, rev up at idle, surge, or just generally act stupid.