Answer to Question 1E.
Energy and momentum are treated relativistically in the scattering.
Answer to Question 2D.
Planck's radiation law depends on

(but even that is incomplete) but does not depend on
T4.
Answer to Question 3C.
The terminal velocity of the drop occurs when the frictional drag forcewhich depends on velocitybalances exactly the gravitational force and the drop falls at constant velocity. The radius of the drop is related to the terminal velocity, and knowing the density of the oil can give the mass.