Yes.
Well, also, it's easier to spin the propeller fast enough to get thrust out of it.
Yes, but it's moving over the ground.
The propeller isn't just spinning. It's being spun. The cart is moving over the ground. This turns the wheels, which spin the propeller. It takes some force to turn the wheels, but the thrust provided by the spinning propeller is greater than this force. So the net force is positive.
See my calculations, based on figures provided by spork and by ThinAirDesigns. (These calculations are for the cart moving even faster than the wind.)
Which don't work and are in total disagreement with the measured trial results. The net force on the cart is a near constant 32N*(assuming 640lb is remotely correct) whereas the calculations show a net force that changes with the ratio of cart to wind speed - and is not enough to propel the cart after losses are considered.
* acceleration is nearly constant.
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