I may be wrong but if you were born in the US, which I assume you were since you hold a US passport but you were registered at birth in Japan in your family registry, I think you can register in Japan as a Japanese because of your parents' family registry. Thus doing so, you will automatically verify your Japanese citizenship.
While living in Japan you would need to live as a Japanese national, paying Japanese taxes, retirement, and the National Health Insurance on your income in Japan. You would also file with the IRS but you would get a $78,000 foreign income exclusion if you qualify. About trading income from the US.....I'm not sure about........