(1) As I tried to point out in the last post of the thread that Intruder cited, the jet and prop cases are extremes on a spectrum that has real aircraft in the middle. With all other things equal, a real prop-driven aircraft's best endurance will probably be higher than Vmp, and a turbo-fan's best endurance will be lower than Vmd. I believe turboprops, like piston-engine driven props, have approximately constant BSFC, so the prop case is applicable.
(2) With usual assumptions about the shape of the drag curve, Vmp is usually at about 70% of Vmd. You need less power because energy is force times distance moved and thus power is drag times speed. At Vmp you have a little more drag but much less speed, so the product, power required, is less.