Just so you know...

Saying South Korea is heavily responsible for Japan's culture, language, religion, architecture, what have you, is like saying Italy is responsible for England's because of the Roman invasions. Baekche is not and has never been South Korea, its language and culture are dead. Korea, like Japan, didn't exist in 200 AD, just a bunch of scattered kingdoms, cultures, and language-families, on both sides of the sea of Japan. Bronze tools, weapons, and wet rice farming almost certainly came to the Islands of "Jomon" peoples via the peninsula, specifically kingdoms along the Western coast, and possibly Goguryeo. These new bronze-wielding, agricultural civilizations in the Japanese islands would displace the Jomon peoples north, absorbing some of their language and cultures when they conquered them. During this time it's as likely that the many fractured kingdoms claimed lands in both the Japanese Islands and the Korean peninsula, but at some point or another, Korea consolidated its kingdoms into Three, and Japan's into the Yamato Empire (supposedly, and probably not erroneously, with some familial relations to the Baekche imperial family; we don't know under what circumstances, long-held, or more diplomatic relations, like those held between English and French monarchs.)

It's frustrating to study the history of early Japan because the written record is so poor. It's like trying to figure out the history of the USA when the written record starts in 1910.