The fan staying on could be a sign of actual overheating, low in coolant or a bad cooling fan control switch. The drivability problem could be many things, unfortunately and without experiencing the problem first hand or being able to do some basic diagnostic tests its hard to say. An engine needs fuel, spark and mechanical integrity to run. Fuel pressure and volume is easy to check (even "opening" a fuel line while someone cranks the engine over will verify the presence of fuel but won't verify pressure). Ignition spark is easy to verify, and after that plugging in a scan tool to the 16 pin diagnostic socket under the dash can verify the operation of a lots of key engine sensors without having to do intrusive testing at each sensor. Many sensors on the engine are shared by both the ignition and fuel system, failure of any of these may cause an engine to stop running. You would need to see if you ae loosing spark or fuel when the engine stalls.