Greetings and welcome to JREF.
Japan does have natural born citizens, but the catch is one of your parents must be Japanese. A chhild born to American parents in Japan is not a dual national, but a child born to Japanese parents in the US is (since in the US, anyone born there is a citizen). See the difference? This lack of natural born citizenship is one of the big complaints of immigrants to Japan who have two or three generations born here (Japan). Though their children/grandchildren might have been born in Japan, speak Japanese, go to Japanese schools, live like any other Japanese, they still must apply for citizenship and go through the process like any other immigrant right off the boat.
Japan doesn't have a "Bill of Rights" per say, but check the wording of
Chapter 3: Rights and Duties of the People in their constitution. Since it was put together by the US occupation after the war, it reads almost the same.
If you are not a citizen, you don't get to vote. This is really the only benefit you are denied as a non-citizen. You can still go on the dole, have to pay pension insurance, and are entitled to such benefits if you work and retire in Japan. I suppose the only other thing you are denied is a Japanese passport, but so what? I like blue better ;-)
I would think you cannot be exposed to being tried for the same crime twice, but the Japanese legal system is not one I am really familiar with. I only know you should do everything in your power to stay out of its clutches.
In my experience, the central government is much, much, much stronger than the prefectual governments. In explaining how things work in the US, I always have to remind people that for things of the division of power in the US and the power of states to make a lot of their own decisions on things like education, budgets, and the like. If Tokyo says "jump," the prefectures ask "how high?"