I recall that originally, Shinto was used as a justification of the rite to rule for Japanese emperors, much like Christianity in Europe. In other periods, Buddhist temples and Shinto shrines were used as a proxy for government administration, while in other times the government actively suppressed the power of Buddhist temples, and in particular it went out of its way to stamp down on Christianity, before once again advocating religion in the early 1900's. Could someone please explain these developments?
while in other times the government actively suppressed the power of Buddhist temples, and in particular it went out of its way to stamp down on Christianity
I can't talk about all of these developments, but I can discuss these two.
The man who suppressed the activity of Buddhist Temples was Oda Nobunaga; one of the most powerful and important warlords of what is typically called "Feudal Japan". Buddhist Temples in Japan opposed Nobunaga militarily and politically and Nobunaga wasn't the type of man who liked being opposed. So, he did what he did with essentially all his enemies: he crushed them.
The suppression of Christianity stemmed from two key things: a suspicion of Christianity, and a rebellion. The Tokugawa Shogunate deeply valued Western trade, but was very suspicious of the religion it brought. There was a "ban" of Christianity in Japan, technically, but it was hardly enforced. In 1637, a rebellion was sparked in the Shimabara region of Japan. The rebellion was actually over heavy taxation during a poor harvest, but the Shimabara region was in a heavily Christian part of Japan, so the Shogunate took interpreted this as Christianity being a force that caused instability. So, Christianity was actually banned, and the main bringers of missionaries, the Portuguese, were kicked out of Japan. The suppression wasn't theological; it was political.