Not all natural things use flapping mechanisms. More recent discoveries find that some bacteria use a rotating flagellum to propel themselves. The motor that drives it is still something of a mystery, with various theories proposed, including stepping-motor function and an electromechanical "cam drive."
Yes, that's correct. But those are at the molecular level where it is possible to have something that acts as an axle. What's interesting is some of them use positive ions rather than electrons (hydrogen and others), the energy source is still ATP. I used to do a demonstration at the Woods Hole summer courses where we could detect calcium ions being used in sea urchin sperm- it is used in the dynein motor proteins.
...and how much of the difference is because natural flyers are optimized for a very different mission under very different constraints?
True, you did mention much slower speeds and lighter weights. Some small model planes do fly under similar constraints (I'm thinking indoor flight, small rubber-band planes, .049 powered planes). Something like a california condor probably is approaching the maximum size, I think, for that design.
