Why did the Crown Prince always live seperately from his parents?
Elizabeth Gray Vining suggests that the court officials cooked it up as a way of keeping the royal family divided and hence their own influence high. Their explanation was that it meant he could be treated more like a normal boy if he was outside the palace (Windows for the Crown Prince pg 36)
Why is the head of the royal family in Japan called an emperor, not a king?
First of all, the Japanese word tennou doesn’t really translate as one or the other (although Japanese does have a totally different kanji Chinese symbol that is usually translated as “king”). However, as it is the same title as used by the Chinese emperor the westerners probably started to use it for Japan too because of its use in reference to China and other Eastern “empires”.