Taking over Indonesia is a direct act of aggression though. It isn't Japan's to take, and I don't see how they wouldn't get a war declaration on them as a result. And even then, why would they let so many Indonesians into Japan proper? Even if they did, I doubt they'd have more than OTL there, and thus not many more Muslims than OTL. Sure, it could radicalise Indonesia, but these Indonesian radicals would mostly be attacking other Indonesians and wouldn't so much be attacking Japan. Like ATL's Hui, it would be seen as an anti-colonial/anti-imperialist struggle as much as it is a religious fundamentalist issue.
As for Japan engaging in Middle Eastern wars, Japan still won't have many Muslims to commit terrorist attacks, and I doubt Imperial Japan would be any more open to immigration than OTL Japan (and if they were, like modern Japan, they'd seek immigrants from non-Muslim countries like Vietnam, etc.). The US has had fewer Islamist terrorist attacks, probably in part because European countries have more Muslims and thus a bigger base to radicalise. While a Japanese "9/11" or some other event is possible, I wouldn't rate it too high on the plausibility scale (9/11 as it was borders ASB luck). Islamists already hate Japan--ISIS killed that one journalist, the Japanese translator of the Satanic Verses was murdered by an Islamist student, and they hate Japan's culture. Attacking Japan, hurting their economy and killing their people, would make sense, but they've never really bothered. I don't see why this would be too different in some ATL. ATL Japanese influence in the Middle East is already throwing a big wrench into things, but I don't see why this Japan would necessarily be too friendly with the US (at least not much more than China is, since Japan and the US are competing over the Pacific and all), plus Japan has Sakhalin/Karafuto's oil, plus they get a lot of Manchukuo/China's oil, and they have investment in their own indigenous oil, and they likely are even more nuclear than OTL (the anti-nuclear movement could be more or less "vanished").