1. Ooh, a very interesting question! I imagine Baizou in a very curious position on all fronts. On the one hand, Baizou's postwar government adopted the Americans' proposed constitutional amendments quite readily in its now longstanding tradition of "just going with it" whenever someone with more guns shows up. So Baizou always had that as a diplomatic shield: our politics are simply what you Americans made them to be. The split between the early-occupation New Dealers and the Cold War-era conservatives is surprisingly sharp. In our real-life timeline, MacArthur decriminalized leftist parties in Japan because they were the obvious alternative to the ultranationalists! And the early-occupation staff were "New Dealers," as some historians have termed them, who advocated the left-ish "New Deal/social liberalism" in the rebuilding of Japanese society. It was later that the ultranationalists started to get back into politics, after a conservative reaction and the onset of the Cold War—but for Baizou, the Americans were gone by then! Of course, just because it is canon that Americans left a left-ish political thumbprint on Baizou doesn't necessarily mean the United States accepts its own role in Baizou's non-conservatism. I don't think it would've risen above the level of diplomatic grief and strong words, especially as Baizou began to play important roles in economics and technological innovation, but "accosted" does seem like a fair characterization. But as far as military enterprises went, the US had so many other fronts and proxy conflicts, it wasn't about to start something in Baizou. Their non-alignment was annoying, but it was tolerable.
As for Japan, I imagine an unusual relationship. Perhaps it's over-rosy, but I think Baizou and Japan's mutual sense of kinship, the terror of the nuclear bombs, and the sense that the US was not forthright about what the nuclear bombs were would all combine to create an unexpected postwar truce between Japan and Baizou. While the conservative governments in Japan might not be fond of Baizou's more left-ish approach to social norms and political thought, Baizou's willingness to criticize nuclear armament—and therefore be a former wartime colony that in the postwar now borderline-stood up for Japan—was enough for Japanese politicians to hold their tongues.
(Baizou's perhaps overzealousness in victim-ifying Japan as a victim of nuclear bombings is treated briefly in Princess Yuu's White Elephants and White Lies book about Pacific War public memory in Baizou. While recognizing the terribleness of nuclear weapons, Princess Yuu has suggested that in focusing on what was done to Japan, Baizona were perhaps too quick to forget what Japan had done—which in turn conveniently made it easy to downplay how Baizou had, albeit indirectly, helped Japan to do it as a slightly-more-cooperative-than-most colony.)
As for the USSR and PRC! I'm... hm, I'm not sure I know enough Cold War history to make a decision on that front. Hm... I want to leeean no? Because in the postwar realignment, the Marxist Party transitioned itself from revolutionaries to reformists, so the kind of communisms I figure the USSR and PRC would front wouldn't quite fit in, even though the Baizoan Marxists insisted that they maintained a sense of internationalist spirt—they just, were going to take things more slowly and be a little more conciliatory to the newly-popular progressive Labors. The revolutionary Socialists did form as a reaction to that, but not right away, so I'm not sure how they'd fit into USSR and PRC fronts. But it may be that I just don't know enough about USSR and PRC involvements in overseas leftist politics to picture how that'd play out in Baizou. ^^;
2. I keep hesitating to specialize topically because I'm interested in too many things, ahahah. ^^; While it's not a topical specialty, I've for awhile been really keenly focusing on public history as a subdisciplinary focus. That is to say, history outside academia, and my interest is especially in museum work!
But let it not be said that I don't also have topical interests. There's just too much stuff I want to study, ahahah. I've dabbled in East Asian history, and I'm personally interested in WWII, the postwar, and public memory of both in Japan. I've also lately put a lot of time into Western American history, particularly gender, religion, and race in the Intermountain West. But even there, I keep splitting myself between centuries and subregions... ^^;
3. Ah, I'm afraid Furudo's sprites probably won't show up in Baizou's cast. I think her design is a little too extravagant for Baizou's aesthetics. Sorry!