1) The compass is not the shortest route between two places but the great circle is.
Great Circle - a circle on the surface of a sphere that lies in a plane passing through the sphere's center. As it represents the shortest distance between any two points on a sphere, a great circle of the earth is the preferred route taken by a ship or aircraft.
2) Off hand, I don't see how it would prove/disprove a FE. If you keep due north on your right, you will travel the latitude (more or less, magnetic N is not true N) on both. Things would probably get funny near the S. magnetic pole as it is far away from true south and the S.Pole.
3) If you want to go absolutely E/W, you need to use the N.Celestial Pole (due north) and S.Celestial Pole (due south) to navigate. That is why sailors used the stars and sextants.
A compass is comprised of 360 degrees. N/S and E/W are STRAIGHT LINES forming 90 degree quadrants. On a FE, E/W is a circle.
Drawing a 90 degree line off N/S line, will always point south on a FE map/compass. How does this work for plotting a E/W course on a map?
The compass degrees do not change.
Due West from my house is Japan. That is 270 degrees on a compass and a straight line. That is how it has been drawn for thousands of years.
That is why older ships used Flat Maps(not FE maps) and compasses to navigate. Yes stars and sextants too. But they had a compass and used it for plotting.
1) Are we talking about true N/S or MAGNETIC N/S? So be clear, which are you referring to? They are different. Longitudes are base on true N/S (N.Pole/S.Pole). Magnetic lines join the mag N/S like a magnet and do not usually correspond to longitude lines. That is what compasses use. That is why typically you need to make corrections to compasses if you want to know where true north/south is.
2) There is E/W that is relative to true north/south that is perpendicular to longitude lines. Compasses use mag E/W that is perpendicular from any magnetic line.
3) Although the E/W lines are perpendicular to the longitude/mag lines, they are not nice rectangles (straight lines).
On a RE, the vertical lines (longitudes) converge at the N.Pole and S.Pole. The magnetic lines do the same at the mag N.Pole and mag S.Pole (that compasses use) but in different places on Earth.
On a FE the magnetic lines converge on the mag N.Pole and mag S.Pole (compass) also. The longitude lines keep on diverging from the N.Pole (the true S.Pole on a FE should be under the N.Pole on the other side). The "edge" should not be the S.Pole but the equator.
4) Japan being E/W... is that compass or based on longitudes?
5) E/W is NOT a straight line anywhere. It is always a circle. On a FE it goes left/right. On a RE, it goes up/down/left/right.
QED: Go to the N.Pole or mag N.Pole. Go say 3 feet (1 m) off it it. Now, with it on your right, walk around the ~9 feet (3 m) to get back to the same spot you started. Did you make a circle? or did you go straight? Does it matter if it is a FE or RE?