Wonder if you have a stopped up fuel filter? Prevents fuel from getting to the engine. Feels like you are running out of fuel while driving because the engine is starving. Not sure where all the filters are but there is one near the primer pump; if it is not clear, this could be the culprit.

When you say the engine does not turn over, it sounds like a dead battery. If you go back and it then turns over, that sounds like you have a loose wire on the battery or starter which sometimes makes contact and sometimes does not.

Or it could be the solenoid in the starter. If it refuses to turn over and you are sure the wires are tight, just tap lightly on the solenoid and see if it turns over.