The first thing you will have to prove in court is that you are the owner of the copyright. How do you plan to do that? Two people can both claim that they wrote their story in the same timeframe, but just stating that is not adequate proof in a court.
If you publish it, the publication date is considered proof. If you didn't publish, then your posting it to a site like SOL (with a posting date) would also be considered proof (though you might have trouble if you modify the story and thereby change the posting dates on either the story as a whole or individual chapters)).
It can get tricky if you publish under a pen-name.
Again, Amazon should have records (i.e. your tax ID number for direct deposit), or SOL would have your original owner ID and a list of your pseudonyms you could supply the courts.
Really folks, this isn't that hard!
I know that in the US there are companies which do this in respect of films etc.
One VERY reliable one is Bowker (in the U.S.), where you can store your original story text along with your assigned ISBN, so you could not only prove it was your, but also the date you first wrote it (instead of merely the publication date).
Would posting a copy to yourself be a cheaper alternative? Either a printout of a short, or a CD of a longer work, kept by you in an unopened envelope (which you'll have put some identifiers on so you know what's in it) bearing a postmark which establishes a hard date.
That used to be a reliable method (150 years ago), but nowadays, it's not difficult to modify dates and text on a computer and save it to a different device to hide the system changes. Thus it's unlikely to hold up in court. It's also a simple matter to steam open the envelop and replace the original contents with something newer.
In these matters, you have to think like both a lawyer and a criminal.
Yes. But evidence of the change might be detectable by a forensic computer specialist.
Not necessarily, say if you transfer the document to another device, where it would create an all-new document without the system clues.
Yes, but not easy to do if you want to fool a good computer forensic person. What's better is to email a copy to another person. That will provide records of the email on the mail servers as well.
Your best bet is to mail it to a lawyer. They'd know not to open or tamper with it. Then it's his word it wasn't tampered with, and most lawyers aren't willing to lie on the stand for a client because they know if they got caught, they could never practice law again.