Why do transhumanists keep setting arbitrary (and frankly nonsensical) "immortality" dates in this century, like 2045?

I'd say it's that people like numbers. As a result, a lot of people pull out arbitrary numbers of much higher precision than is reasonable.

And three, why all the focus on this century for people who aspire to live a lot longer than normal?

I don't think there's much point in focusing on that stuff other than entertainment. I guess people think it's more fun to think about how things will improve in a century or so than to try to work out what completely alien world will exist in the distant future.

If you do think it will be useful, then you know more about the near future, so you can think about it more productively, you have more time to think about the distant future and you can procrastinate, and thinking about the near future will pay off sooner, so it will better compete with investing.