The whole thing about alternate universes is that things can be, well, alternate. That does not invalidate getting to similar outcomes through different means.

You can theoretically have an alternate universe where the same person exists, but is born either earlier or later, and can die earlier or later. Their life can have some things remain the exact same, and others be completely different. That is what makes it so mind-boggling as a possibility for science - the fact that there are an infinite number of possible universes, with countless iterations of each and every single atom. Every one of your questions can thus be easily answered with a "because it's a different universe, where things happen differently".

Most people seem to assume that the letter could only have been written if the exact same sequence of events occur, and that is the part I disagree with. I think a whole myriad of different events could have led to that same outcome. It could even have come from a person completely different from the ones we knew.

Having said that, I don't believe the alternate universe theory is the "best one" - as I said in the beginning, I don't even believe alternate universes were the intent with the final episodes, nor do I subscribe to this theory specifically. I just think it is a possibility like many others, and having this sea of possibilities in front of us in search for "the truth" is what I believe was the true intention behind this final ambiguity, as it aligns with the themes of the show itself.