Does living in Japan and being a Japanese citizen (with a Japanese passport and Japanese Permanent Residency) help me at all compared to the Indians living in India, U.S, U.K, etc? Am I considered Japanese or Indian?
In many cases there is just one box for Asian that you would mark either way. If by some chance it does have more breakdowns then your ethnicity would be Indian. If it asks for your country of residence or citizenship then you put Japan.
No. Both Japanese and Indian fall under Asian, which means you are at disadvantage either way.
In any case, nationality and racial background are different things.