The three countries that influenced Japanese culture in the Heian period were, India, Korea, and China.
Religion, Art, Music, Clothing
China and Korea
The United States has had an effect on Japanese culture, with some major changes coming about as a result of the Allied Occupation of Japan from 1945 to 1951.
The Japanese borrowed ideas such as writing system, architecture, Buddhism, Confucianism, and government structure from China. The adoption of these elements greatly influenced the development of Japanese culture and society.
China and Korea mostly. China by obvious reasons (Written language and other customs such as the lunar calender, etc. Japanese culture is hugely based off of Chinas) and Korea had other influences as well (Brought over technologies such as paper printing, pottery and art, etc). It's important to note, in the earlier days Korea had more of a direct impact whereas China had more of an indirect one (When Koreans introduced their culture, they also introduced Chinese.) Soon, Japan was able to have relations with China directly
The Asian cultures of China and Korea greatly influenced Japan. These two cultures are close to Japan. Korea has served as a bridge (of cultures) between China and Japan.
I know one of the major things China influenced Japan on was religion. China helped bring Buddhism to Japan. In fact almost the entire country is Buddhist or Shinto (A derivative from Buddhism that the Japanese formed over the years).
Japanese Art has been influenced by many countries, but most notable was China.
Japanese culture was blended with Chinese and Korean culture. Chinese adopted budhism from India which was later spread to Japan. Korean influence can be seen in Japanese paintings and architecture.
China
Yes, Japan's culture was heavily influenced by the Han culture.