Q: What defines a single bladed rotor? Would a single stick of wood projecting out horizontally from the body be considered a "lifting surface" that "rotates on a common path around a vertical axis"? (section: 3/ paragraph:  f/ sub-paragraph:  / line: 2)

A: No, that would not be considered a lifting surface. To be considered a lifting surface, it must contribute lift to the overall flying assembly. An easy way to demonstrate that would be to demonstrate flying it with and without the surface, if the surface is not present then the flight would be significantly different.