at the moment it quits, check to see if you have spark at the plugs. if you have good spark, then pull the drain on the carb fuel bowl. should be able to get a steady stream of fuel. if not.. check for tank vacume.. and stuck float..e tc. you can rap a screwdriver handle onthe side of the carb and see if it make sit flow.
ont he popping sound, is it brake dependent? does it go away if you press the brake? how about if you pull the pedal up?
any oil leakage from that axle seal?
have you checked all lugnuts and rim to center bolts/nuts?
i'm not as familiar with that early hub and axle design.. but if none of hte other panned out..i'd be be checking the bearings.
jack her up and se eif there is considerable play. might be bearing pop.