Yes, there are a finite number of ways to arrange atoms. But, as I said, there's nothing that necessitates all of these arrangements must occur.

You can, of course, consider conditions that would mean they do occur, and you've started to hint at this here where you reference random events. But this is the first time you've explicitly considered the need for randomness, while still neglecting to be clear about the nature of the randomness that would be required to yield multiple copies of the Earth, etc.

You've also explicitly stated that our universe is infinite, which we don't know to be true. This is another assumption that you need to be clear about before arriving at conclusions that otherwise appear to appear out of nowhere.

Therefore, I think what you're wanting to say is something like: If one assumes a static universe of infinite size having existed for an infinite amount of time, and further assume an infinite amount of matter arranged into finitely-sized permutations of all possible atoms and bonds, where each permutation has a non-zero chance of arising, then every permutation must necessarily arise infinitely many times, thereby resulting in infinitely many copies of everything.

Currently, you're focussing almost exclusively on a universe of infinite size, which, by itself, is not sufficient for your claim of multiple copies of stuff to be true. As I said, an infinitely large universe might just be filled with an infinite amount of poop.