Is it valid to ask about fanfic and other alternate-version sources for science-fiction material on this site?
I can't think of a reason why not. Seems to me that scifi is scifi, whether written by established authors or by fans. Now if you're looking for canon, that is a different story.
Fan fiction, therefore, is defined by being both related to its subject's canonical fictional universe and simultaneously existing outside the canon of that universe.
There is no notability requirement on this site. You can discuss works that haven't been published professionally, including fan-fics.
That being said, please don't post questions that no one in the audience had any chance of reading. A question about a fan fic that's only ever been distributed on flyers at Gryffon†Con 1942 would be too localized.
Posting a question just for the sake of promoting your own fan-fic is not appreciated, like any other self-promotion question on Stack Exchange. For writing advice, as per this meta thread, go to Writers Stack Exchange.
I generally agree with morganpdx. However, if there's any question of fanfic that's in violation of copyright, we should probably avoid linking to it or discussing its content (as opposed to, say, discussing its status as an infringing work) to keep from performing contributory infringement.