Map projections: every flat map distorts

Questions

1. 1
   Not answered. Why is it impossible to flatten a sphere onto a plane without distorting something?
2. 2
   Not answered. What does Tissot's indicatrix on a map represent?
3. 3
   Not answered. On a conformal projection, what do the Tissot indicatrices look like?
4. 4
   Not answered. Which statements about the Tissot indicatrices of an equal-area projection are true?
5. 5
   Not answered. Writing a and b for the semi-axes of an indicatrix in units of the map's nominal scale, which relationships hold?
6. 6
   Not answered. On a normal-aspect Mercator map, by what factor is the area of a tiny shape at 60° latitude exaggerated?
7. 7
   Not answered. Can a single projection of the whole sphere be both conformal and equal-area?
8. 8
   Not answered. What is the name for the shortest path between two points on a sphere, formed where a plane through the center cuts the surface?
9. 9
   Not answered. Two airports sit at exactly 50° N. What does the shortest surface route between them do?
10. 10
    Not answered. An in-flight display uses Mercator. The route follows the shortest path, yet the line appears as a pronounced arc. Why?
11. 11
    Not answered. What does a straight line drawn between two points on a Mercator map represent?
12. 12
    Not answered. Which projection draws every great circle, and therefore every shortest route, as a straight line?
13. 13
    Not answered. An azimuthal equidistant projection is often described as "preserving distance". Distance from what?
14. 14
    Not answered. Which of these characterizations of well-known projections are correct?