Yes, there are exceptions. But for most of history the crown prince, is in fact the best person to rule. All of those instances are meritocratic? We'll admit the occasional error but would you at least say that bloodline aristocracy is often meritocratic by your definition?
>From how you have spoken, I think you would count this training as privilege and not something that increased merit.
Correct. If in Azad society my parent's wealth or the high school I attended had a significant bearing on my skill at the game then I would say that is not a meritocratic system.
>If we had a similar test that accurately predicted future success and job applications were decided by this test, would that be meritocratic?
If it was able to remove environmental and structural effects then yes, that would be meritocratic.
>Would that change if parents were able to send there kinds of a special $10k/yr school that significantly increased their children's results on the test?
Absolutely it would change. It's no longer a measure of merit, now it's a measure of merit AND your parents' wealth AND your parents' willingness to spend on your development. We can't separate out those factors so the test is now useless as a measure of merit.