1. Can I sponsor him as common-law partner while he will be studying in Japan, in Feb 2023, although I wont be living with him? At the time of sponsorship, we would have met the one year co-habitation requirement since Nov 2022 already.
Yes, the fact that you were common law prior to applying means still eligibile (as long as relationship maintained). Also note, you can apply from abroad to sponsor because you are a citizen (i.e. before you return to Canada). You'll have to show evidence of intent to return to Canada (and then update when you do return is best way to go ahead).
2. Those who are in similar situation as us, what kind of evidence you usually submit to IRCC?
I did not apply as common law but only because we were able to get married, so familiar. (Not same sex either but that doesn't change anything).
The key things to keep in mind: you MUST show strong evidence of the beginning of your time living together and the twelve months continuous. A day less than one year means not common law (so it's not ideal to apply the day after you become common law, more time does help).
This can be hard in some countries - eg if no lease or other third-party evidence of residing together. Make sure you document your cohabitation extremely well. Just go through the list of things you can show and do what you can. (You can explain if you do not have some of them - but it's up to you to demonstrate you meet the common law test.
For that reason, it really, really is worth considering whether you can get married somewhere - not easy in your situation and up to you, but it does make the minimum test easier. Legally married plus mediocre evidence of cohabitation is a pretty strong case (all things being equal); not legally married plus mediocre evidence is a much weaker case and could be refused on basis of not meeting common law requirements.