Ojo
I currently live in Tokyo, Japan. I am a US citizen but have been here for 5 years. I am not a lawyer (worse, an accountant) but I believe I understand the basics.
The US will not allow dual citizenship so metooxx is correct that if you are currently a US citizen (which it sounds like) you cannot become a Japanese citizen unless you give up your US citizenship.
If you stay a US citizen, then unfortunately, you cannot escape US taxes either on your trading in the US or on any salary, etc. you earn while in another country. Of course the rules are somewhat complex.
As for Japan taxes, you will only be taxed here on amounts that relate to work performed in Japan, thus, you would not be taxed for any trading gains/losses related to your US trading. But currently this only works for the first 5 years and after that you become a "permanent" resident and you will be taxed on any form of income (including trading gains/losses from the US).
Hope that helps. Also, broadband services are currently cheaper than the US (about the only thing cheaper) and Japan is way ahead on wireless applications.