How did Japan preseve its identity and culture when the Chinese Empire had such a great impact on the surrounding areas around 200 A.D.?
There are precious few good historical records of Japan in the period under discussion, circa 200 AD. Japan's is an ancient civilization, going back thousands of years. While the Chinese emperors were certainly powerful, political turbulence characterized by violent rebellion characterized the transition from the Qin Dynasty (221 BC-206 BC) to the Han Dynasty (206 BC-220 AD). While the Japanese would eventually pay tribute to the Chinese emporers, Japanese political and military developments helped to ensure its independence from its larger neighbor.
The Yayoi period in Japanese history (roughly 400 BC to 250 AD) saw an evolution in Japanese society toward a more modern era, as agricultural practices and the use of iron and bronze in the manufacture of cooking utensils and tools enabled the people to subsist better than before. China, preoccupied with its own political intrigues, did not see Japan as either a threat or an opportunity. By 250 AD, the Kofun period in Japanese history witnessed the growth of powerful warlords and military states and the beginning of empire within the confines of island frontiers.
Japan was sufficiently geographically isolated that it would be many years before outside powers would begin to view it as an opportunity for exploitation. The Chinese, meanwhile, were more interested in expanding and consolidating their hold on the Asian landmass that is today China.