Japanese adopted the "traditional" Chinese characters and their system evolved from that point. Both Chinese and Japanese characters underwent a simplification process from those original traditional forms, but the simplications aren't always the same. Japanese also has hiragana and katakana, which are syllabic and phonetic and often used to represent foreign names. So the short answer is that no, you can't simply use the Chinese unicode block, whether traditional or simplified, to represent Japanese.

Korean uses Hangul, which is an alphabet and entirely unrelated to Chinese or Japanese.