I will give my opinion regarding Japan-South Korean (Korean) relationship.
South Korea or let me say, Korean peninsula as a whole is naturally and historically have a mutual cooperation (in Economics) and dependence (as a country and foreign relation context) with China. Several times they prefer to giving their tributary gift for the Ruler in Mainland China and several times they are very against to acknowledge Japanese overlord over them, especially in context of Imjin war era. Their ruler and peoples will be much more comfortable to joining side with the Chinese in future rather than with US and Japanese side. After all, they see Japan as a threat rather than potential allies.
I can understand the sensitivities of the Koreans. The Chinese , understandably, had a cultural and economic influence on Korea. Tho I will say there were times when Chinese dynasties such as the Tang, had fielded large armies in the attempt to force its political will in Korea. But for the most part, largely that is, China and Korea had a historically mutual benefit. Even when China was conquered by the Mongols (Yuan Dynasty), the Koreans , as vassals of the old system and thus remained vassals of the new political machination, fielded troops for the Mongol Khan , to support the invasion of Japan. In fact, in the 2 failed attempts to invade Japan, a large part of the Mongol expeditionary force / fleet were mostly Korean and Chinese soldiers with Mongols being bannermen and officers.
Japan, under Hideyoshi, conducted an brutal war in Korea. So, that was largely retained by the Koreans in memory. Then our intervention during the Sino-Japanese War, and then the Russo-Japanese War. Japan took the opportunity to annex the entire Kingdom of Korea into the Japanese Empire. Imperial colonization took effect, as it did much in Formosa, Kuril, and Korea. The Koreans have historical basis for resentment. Tho i will premise that Japan contributed greatly for the education , industrialization, and overall demography in Korea, to the national psyche, they (Koreans) cannot get over the fact that they were conquered peoples. They still hold deep resentment on that. And I can empathize. However, it should be stressed that the past is the past. Japan no longer holds any idea or even an inchling of any Imperialist agenda. he he!
Budhism is also Indian, boy.
Infact Budhism is considered by many as one of the philosophies under the aegis of Hinduism.
Yes this is very true. Many great religions have come out from the Greater Indus Valley Civilization. These include Jainism, Buddhism, and Hinduism.
I would infer , however, that Buddhism , like any theological thought, has various schools and sects. There is Mahayana Buddhism, there is also Thervada Buddhism. In fact, Thervada Buddhism was more so apparent in South East Asian states such as in Cambodia, Laos, Thailand, Burma; and they were influenced by Sri Lankan (Sinhalese) Buddhist monasteries.
The Buddhism that is practiced in China, Korea, Japan largely is a synchronized and synergized belief system. Buddhism in these East Asian states are molded with the prevailing Confucian concept(s), as well as even seen in harmonious union with Taoism / Daoism (as in the case of China, Taiwan, and some parts of Korea). For Japan, however, Buddhism is merged with our own native Japanese religion that is Shinto. In fact, there is a trilineal union of Buddhism, Shinto and Zen spirituality. Known collectively as Zen-Shinto-Buddhism. Its rather an interesting concept. East Asian civilizations tend to adapt foreign concepts and apply it to the native land's perception and needs.