Resetting the light and getting to inspection before it comes back on won’t work. You will then fail because the computer hasn’t finished running all of its tests. There is no way to trick it.
The P0130 refers to an issue regarding one of your O2 sensors. The normal thing to do is check the wiring/harness for the sensor, check for exhaust leaks, and vacuum leaks. If none of that indicates any problem then you probably just need a new sensor. Nine out of 10 shops would just throw a new sensor in there without checking anything.
The P0496 is probably related to your trouble starting the car after getting gas. It is for the evaporative emissions system and has to do with a problem with the purge flow (when the gas fumes are sent to the engine to burn). It basically means that evap flow is detected when its not supposed to be. I hate to tell you but those codes often turn into fishing expeditions. You need a really good diagnostician. If you’re lucky you just need a new purge valve.