First of all, relax and don't be too tense.
1. Does Korea have some kind of electronic travel record that you can access ? I would not be surprised if they went all digital, which would justify them having removed stamping passports directly, they must be keeping records somewhere and hopefully those records are accessible electronically (rather than you applying to the Korean consulate or embassy).
2. Weird, I suppose those are the pit-falls of a templated letter. Assume that the period is the 5-year eligibility period as a safe-guard. That's what the determination of your eligibility is based on.
3. I know that you can access your US travel history online directly. It's called the I-94. It should have your arrival and departure dates logged in there for a period of 5 years. I actually printed mine when I went for my interview and gave it to the officer who interviewed, he was appreciative that I gave him that. Plus I think that it shows you as the applicant have nothing to hide since you brought it yourself and it helps them to double-check their records and your travel history.
4-5. Aaah, that's probably why you got this request in the first place. You have a name-sake in Canada and they want to cross-check that it is indeed not you. I suppose this is to ensure they don't count trips that *you* didn't go on. Just explain that this is a case of mistaken identity on IRCC's behalf and that you are [your name] whose passport is [relevant passport information]. It's probably a procedural thing, if it so turns out that there are 2 individuals with the same name in the country, have the applicant supply further evidence to make sure that the applicant can be uniquely identified and therefore all the procedures can be run on the applicant and the applicant *only* in order to make a determination on the application.
Admittedly I have no idea if you can just go the IRCC office to explain your case, maybe ask over the phone and explain your situation and request for an in-person interview again, see how it goes ? In any case, my advice would be that you just calmly explain to IRCC that the information that they sent to you is that of a different person, you are not that person and the evidence (such as travel records, entry/exit records, and so on) will show it. It's clearly a case of mistaken identity and IRCC needs evidence to make sure they don't use information that is NOT corresponding to you in order to reach their decision on your application (which is the correct thing to do).
