A little maintenance goes a long way although you may have larger issues. Get new spark plugs even though theres only one(note condition of old). Clean n adjust points, oil felt pad, Common mistake on sha carbs is running the throttle cable thru spring(it does not) and clean idle hole under slide. Ensure choke releases upon wot. Ensure the metal filters are there.
There appears to be lotsa fuel leaking down and out your exhaust, also appears to be lotsa buildup on the bottom of your cylinder. Could be a handful of items, float needle damaged not sealing, dirt grime, add inline fuel filter, loose head bolts, leaky crak seal, etc.
To zone in on fuel or electrical problem,test for spark when it dies. If plug wet then, No spark with fouled plug then try a new one, plenty of spark with new plug means fuel issue. If new plug, moped starts right up then its an over rich condition.