Have a Repair Shop Diagnose the issues.
Simply can not guess or diagnose over the internet,
without looking at Vehicle Data & or Testing some Components.
To guess I would start with the Evap System possibly having a failed
Solenoid but that may not have anything do with starting & not starting
during or after Filled the Gas Tank may be totally unrelated,your just discribing
a Symptom that may not actually point to a starting point for testing.
I would be inclined to look at Vehicle Data,pull a couple spark plugs,look at
O2 Sensor & Fuel Trim & Evap System Function as mentioned & gather
some history about your vehicle & what has been done & possibly never
been done in the way of Maintenance.
That is a very small engine,you have a timing belt,turbo & all sorts of things that
simply just don't last long or work well for many years,so the possible reasons
for your concern could be multiple problems.