The Big Freeze seems more likely than the Big Crunch to me. It's also the only fate of the universe that's possible regardless of what its ultimate shape is, as it's solely reliant on time (and physics, obviously). And crunching in general just seems illogical, isn't the universe expanding more rapidly now than it initially was after the big bang? Unless I'm mistaken, Newton's first law would have to be thrown out entirely in order for the increasingly rapid expansion to not only stop, but reverse. It really makes me doubt the theory of a closed universe in general.
Anyway, yes, the logic in the first post is flawed. The subset in this infinite set is still infinite. For comparison, if you have an infinite set of numbers, if you made a list of all of the numbers that included a 1, you would still have an infinite amount. This mirrors the planets theory as there is nothing inherently limiting life to specific planets (unless you are religious, I guess?), so with an infinite amount of planets, even if only a "fraction" of them sustain life, you are still looking an infinite amount because there is a chance of it happening.
You can have a finite subset for an infinite set, but such a set has to be explicitly stated. In the case of an infinite universe with infinite contents, the only way something could be finite is if it occurred or was created with no possible chance of the event or creation reoccurring. I don't think that's possible within nature, or even at all. The closest thing we have to a finite existence would be a synthetic element, but even those might exist elsewhere in the universe where conditions are different than here on Earth. Who knows.
I think all of the above is correct. Unfortunately, I never got to take any classes that got into this stuff so something (or everything

) may be off.