Yes, although contest rules to date haven't yet motivated doing both at once. In F1D international competition, propellers are commonly variable pitch (Indoor Model Airplanes: The Best of Indoor News and Views, ed. Tim Goldstein, pp. 138-144) to better exploit the gradually diminishing power during a flight, and sometimes variable diameter (ibid., pp. 119-126) to reduce drag like a folding propeller would. Although not a contest winner, R/N Models' "Maverick" kit included a folding propeller purely for drag reduction.
No: if you need variable pitch for efficiency from a variable-power engine, and folding for drag reduction, it's simpler to reduce drag by feathering (changing pitch so far that the propeller won't windmill while unpowered) instead of by folding.
No, for a special case: For propellers of the size you show, 8 to 16 inches diameter, 300 to 2500 watts electric power, a typical flight profile alternates full power climb with zero power glide (hopefully finding thermals to stay aloft). Partial throttle only wastes energy. Proving that mathematically is hard, but it has been verified with numerical simulation. "Cruising" is best done with a burst of climb (what the propeller is best at) followed by a long glide (what the wing is best at). At any rate, for a full on / full off power source, a single pitch is optimal.