As I recall, we didn't measure the deflection angle directly-but using some kind of interference fringing effect where some of the light from the original laser was interfered with the light entering the microscope-noting how the interference fringing changed allowed more precise calculation of the deflection of the light beam.
12.
It's impossible in the same sense that you can't make a practical perpetual motion by building a wheel with a perfectly frictionless axle and spin it in a perfect vacuum and put it somewhere infinitely far from gravitational sources to make a wheel that would ( theoretically ) spin forever-there are just too many teeny-tiny fringe effects that you could never eliminate them all.
