What model is this strange airplane-helicopter combination?
It is a Pitcairn PCA-2 autogiro. From the linked article:


  This aircraft is a Pitcairn PCA-2 autogiro, S/N B-12 (ATC #410), manufactured in April 1931 by Pitcairn Aircraft, Inc., Willow Grove, PA. It came from the factory with a Wright J-6 engine (S/N 12528) of 300HP. It had a Hartzell steel propeller.  It was a three-place craft, weighing 3,000 pounds.


Apparently, the aircraft was owned by Amelia Earhart and sponsored by Beech-Nut packing company.


  NC10780 was sold to George Palmer Putnam, husband of Amelia Earhart, of New York, NY on May 7, 1931.  This autogiro is the “older” (by a week) sister ship of NC10781 flown through Tucson by John M. Miller.