1) Poverty and Low Education Don't Cause Terrorism
2) As long as Japan retains stringent immigration controls and naturalization requirements, it will never have a large Muslim population. In which case, we will not be able to draw any conclusions for how Japan can "live peacefully with Islam," because it's actually not doing so.
How is it stringent when we are mainly implementing the same kind of immigration policies as the United States? I think the better term to use is 'selective' requirements.
Japan does accept limited number of refugees, but immigrants that are brought into the country are professionals, that will contribute to the JAPANESE society. Period.
And we do have a vibrant Muslim community in Japan.
Japanese Muslims, Islam in Japan : JapaneseMuslims.com