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To answer your specific question in edit 1, both the Republic of China and Japan require people naturalizing to renounce their existing nationalities (if possible) as a precondition of naturalization.
The question in edit 2 is very vague. If you are asking about all the situations in which a person has those 3 nationalities at the same time, the ways are too numerous to list. We can begin by considering each country's nationality rules.
So in the case of Japanese, US, and Canadian nationality, that can happen for a child in many ways, for example, if one parent is Japanese, the other Canadian, and born in the US; one parent is Japanese, the other American, and born in Canada; one parent is Japanese, the other Canadian and American, and born anywhere; etc. Note that such multiple nationality will not last past age 22.
Similarly, in the case of ROC, US, and Canadian nationality, that can happen for a child in many ways, for example, if one parent is ROC, the other Canadian, and born in the US; one parent is ROC, the other American, and born in Canada; one parent is ROC, the other Canadian and American, and born anywhere; one parent is ROC and Canadian, the other parent American, born anywhere; one parent is ROC, Canadian, and American, etc... Or the person may be born with only ROC nationality, and then later naturalize in Canada or the US (in either order); or born with ROC and Canadian nationality, and naturalize in the US; or any such combination. Here the multiple nationality is not automatically lost upon any age, and once the person has ROC nationality, they can get others without jeopardizing ROC nationality, so there are more possibilities, as long as they start with ROC.