Put point A on the North Pole (say the upper left corner), point B on Los Angeles, and point C on the South Pole (say the bottom left corner). The Mercator map is wrong in all stations where Los Angeles is not in alignment with points A and C. The idea that we need to change the orientation of the Mercator map to get the angle we want shows that it does not really represent accurate angles
A) The map is not correct outside of the bounds of 82N to 82S, as mentioned in the link I posted.
B) The other angles you are mentioning are definitely still preserved. Just because you don't seem to grasp the fact that one direction is West and the other is East so they'll obviously have different angles, doesn't make them suddenly not work.
C) Yes, you'll need to shift the center point of the map if you want to find, for example, the Westward angle from Cali to Japan. Any non-continuous map will have such issues. I would presume on a ship or somewhere that need it the map would be repeated so you could simply scroll it to the correct spot to find the angle you want.