Here are my answers...
1) you switch your posting when you're reversing directions, but in that case, there is no outside or inside. However, the only time you're supposed to post on the wrong diagonal is when you're going for your Vitory Pass at a horse show.
2) The mane falls on the right side, because in the medieval times, the soldiers/knights used to carry their swords on their left hip. When they were riding their horses, and when they had to pull out their swords during battle (done by reaching the right hand over to the left hip), their sword used to get caught in the manes that were on the left. So they forcefully made the mane fall on the right to prevent entanglement. The tradition just became a standard over the years.
3) They carry their whips on the inside, because carriage driving began in England. In England, they used to have bushes and hedges on the outsides of the roads. When they were carrying their whips on the outside, their whips repeatedly got caught on the bushes. That's why they decided to carry the whips on the insides.

interesting, eh.