Canada isn't really relevant to the plot aside from that one singular mission. It's probably safe to assume that it eventually fell to the Soviet conquest of the states, and that only a sparce few territories managed to live on for just a bit longer. Aside from one radio station where the Pacific Front and European Alliance are coordinating their consolidation of the American war assets, Canada doesn't really have any big tactical involvement in the war. Not that it really needs any, if every location that was relevant to a faction needed to be covered, we'd probably have more info on places such as Siberia, or Mongolia.
Also, wasn't the Psychic Beacon in China provided by Yuri, in an attempt to broker good faith so he could obtain technology from their raids on Kanegawa during Think Different? If I remember right, his sabotage of it was also planned from the beginning, as it would lead Chinese command to contact the Soviets with a desperate plea to free their own forces from rebel control. This was intended by Yuri to weaken the alliance between two countries that were already barely allied to begin with; the fact that China had a Psychic Beacon- knew what a Psychic Beacon was to boot was grounds for concerns from Soviet High Command, as nobody outside of their inner circle should know about them. China knew things they shouldn't, and was likely acting outside the directives of the alliance.
This led to Russia exploring an area of Japan where the Chinese were supposed to have captured and turned over technology for the combined war front, but when they arrived they learned of the Chinese's deception and treachery. Norio made a temporary Non-Aggression Pact with the Soviet Commander to push back the Chinese, since they share a common enemy for the time being. It's assumed Norio manages to escape after the events of Unshakeable, as he isn't mentioned coming under harm between then and Stormbringer.
As for this whole pact thing between the Chinese and the Pacific Front being a thing from before the war, you're right in that doesn't really make sense at all because it's only ever brought up that one time. However, it is not confirmed fact; in the self-same briefing, Norio mentions that he believes that was the case, it might very well not be. Perhaps there's something else that's going on that caused a NAP between China and the PF. For all we know, the treaty may have been signed during the Chinese invasion of Japan, some time after Think Different, but before Singularity, since it's very obvious that China and the Pacific Front aren't allied in Think Different. They may have surrendered because China managed to put them in a stranglehold, and they signed an agreement that allows China to take their technology in return for sparing them. At least, that's what makes sense to me.
South Korea and North Korea were probably always at each other's throat, regardless of whatever their greater armies were up to, and all it took was just a small spark from Yuri to undo the entire, faulty alliance.
Australia was probably just part of the Pacific Front, but not really associated with the greater dealings of China and their bullshit, considering how far detached they are.
Does it really need more explanation than that though? The two remaining super factions of the Allied Forces saw the United States get overrun, and were effectively like "Oh fuck, we're next if we don't fucking crack the fuck down". So they loot what they can from the doomed and dying husk of the American arsenal to bolster their own armies and defense. Selfish, yes, but not something unexpected when you just witnessed an ICBM detonation in what was supposedly the strongest nation in the world, and effectively cripple whatever they had remaining.
