I was just wondering, if I at some point manage to get a short story published somewhere, can it still then be used as part of a novel? Would that novel be able to be published if part of it is already available to the public?
Yes, you can. All rights revert back to the author of the piece once that piece has been published. All legit markets say something like that in their guidelines.
Thirdwind is correct. You'd want to read the publishing contract for the short story carefully. The vast majority of magazine, anthology and ezine markets have reasonable contracts that don't tie up a story for more than a year. Most permit reprints of a story shortly after it reaches publication. With that in mind, if the contents of a short story are included in a far larger work ( a short story being 5000 words or less and a novel being 80,000 words or more--yes this can vary but just making a point), the novel would not in any way be considered a previously published work. The structure of a short story is far different from the structure and contents of a novel, so the length isn't the only factor.
"2001: A space Odyssey" was written by Arthur C. Clarke to accompany the release of the film of the same name, which was based upon Clarke's short story "The Sentinel"