RE: Engine I.D.
Definitely a Nelson, looks like a .15 quarter midget engine. From the looks of the rusty plug, I would be suspicious of the bearings and crank, too - unless someone had the internals oiled well.
I still have the two I used to race with. They used a straight section of pipe as an exhaust, maybe 3 1/2" long or so, just going from memory.
They sure sounded cool.. but hearing protection was needed when you started one up!