1. My financial sponsor was my "Aunt's Fiance" and I had no problem*. Though being American I think they give me an easier time. Some schools require your financial sponsor be a parent. I don't think you have to produce any papers proving your relationship, however some schools want to interview your financial sponsor.
2 & 3. The way they evaluate visa applications is not very transparent, but your financial sponsor being in Japan may be a plus. The fact that you've been to Japan several times and not had any problems (e.g., been arrested, overstayed your visa) may look reassuring to whoever reviews your application. These are just icing on the cake though, your financial ability and lack of a criminal record seem to be the main items of interest.
As I don't work for the ministry of justice, these are only my impressions and they may be wrong.
Good luck!
a7mouse
*I do have a hunch that the school might have put my 'aunt's fiance' down as my 'uncle', but I have no proof of that.