Are questions similar to ones posed here http://tvtropes.org/pmwiki/pmwiki.php/WMG/HarryPotterAndTheMethodsOfRationality
considered appropriate for this site?
Are questions similar to ones posed here http://tvtropes.org/pmwiki/pmwiki.php/WMG/HarryPotterAndTheMethodsOfRationality
considered appropriate for this site?
Here are all of the unresolved questions in the last Harry Potter book - how do you think they will be resolved in the next one
I see three separate problems with this - one that's easy to fix, one that will probably lead to close-votes, and one that's very likely to lead to closing:
(Harry Potter spoiler)
Who Killed Albus Dumbledore?
There's no way to definitively answer this (e.g. which answer do you accept?). There are other meta questions that discuss this, e.g. 1 and 2). I think the outcome here would depend a lot on the question. If it was possible to give answers that drew conclusions based on the material (and possibly other data), then the question would probably survive. If the answers were all just guesses, with little or nothing backing them up, it will probably be quickly closed.
Questions that age badly aren't generally liked. As soon as the next volume/episode is out (which in some cases could be only a few days) the question becomes rather pointless, since there is a definitive answer. If the question was speculation about something that isn't going to have a future volume/episode (e.g. about something that was left unresolved at the end of a book/movie/TV show), then this wouldn't be an issue. For cases where there presumably is going to be an official answer, my guess is that the closer that date is the more likely the question is to be closed (e.g. if it's about next week's episode of BSG then it's certain to be closed, and if it's about a Harry Potter book to be released in 3 years, then it will get a few close votes, but not nearly as many).
(There's also the open question of question fantasy is on-topic, but I'm assuming that the choice of Harry Potter isn't relevant here, and that the question would be the same with more sci-fi material).
There are good speculation questions and bad speculation questions. I invite you to read the section “What kind of questions should I not ask here?” in the site's FAQ, and to follow the link to Robert Cartaino's six guidelines for great subjective questions.
The questions you cite are self-labeled “wild mass guessing”. Wild guesses are firmly in the bad subjective category, because
On the other hand, puzzling out what an author meant from actual clues can be good subjective: