Q: Runs rough & Engine light

The codes being set should be investigated first unless they implicate systems or components that clearly are irrelevant as "causes" of a rough running condition in which case you would diagnose and fix the rough running condition first and then resolve the codes. Whether the codes are, in fact, possible causes depends on what the codes are. The "re-set" you describe is interesting as it perhaps points to something going on with the fuel system. When you re-set the computer, fuel trims are lost and so if the car runs better with the trims erased, obviously that is a clue. You can use a scan tool to read the fuel trim values, once they re-establish themselves after the car runs for a while, and see if the fuel trim is on the high or low side. If there are no relevant codes, the standard procedure is to use an automotive scope and examine the secondary firing patterns to distinguish between a fuel or ignition issue. You can also just sequentially test for all the most common faults, namely a faulty mass airflow sensor, faulty engine coolant temperature switch/sensor (typically at cold start only), worn spark plugs, wires or defective ignition coil(s), inadequate fuel delivery or pressure (clogged fuel filter, injectors), contaminated or old gasoline, defective throttle position sensor, faulty idle air control valve, leaks in the EGR system, intake vacuum leaks, and so forth (many possibilities). If you request an engine stalling/rough idle diagnostic the responding certified mechanic will get this resolved for you promptly. If you have further questions or concerns, do not hesitate to re-contact YourMechanic as we are always here to help you.