Did the Doolittle raid run their engines over square?
According to this transcript of the actual mission report from one of the pilots, they did indeed run over square


  I flew the last 500 miles into Tokyo at altitudes ranging from 1000
  feet to 4000 feet in order to fly in the thin overcast and clouds to
  avoid detection. I used 28 inches of manifold pressure and about 1370
  RPM and indicated between 150 and 165 MPH.


And for the latter part of the mission 


  I made the trip from Tokyo to China at about 500 feet altitude and
  1300 RPM and started at 29 inches of mercury and gradually reduced to
  25 inches as my gas load reduced. I indicated about 160 to 165 MPH.


Question 2: According to this copy of the manual (page 155) the engine is almost always run over square in cruise. 



As for question 3 you can find a discussion on operating over square in this question and ill avoid answering it here to keep it form being a dupe.