Are users allowed to ask questions that deal specifically with fan theories, and that cannot be answered by any concrete evidence?
In short: if your question is likely to start a discussion or debate, it's probably off topic. If your question has a "right answer" that're you would recognize when you see it, it's probably on topic.
This is a bit of a grey area on this site, because as a general rule we don't like questions that invite speculation or opinion. So we are probably not the place to ask about a brand new interesting idea that you have about some work of fiction. If you're goal is to "chat" or "discuss" your particular theory with other people, then don't ask a question on the SF&F site.
(You would be welcome and encouraged to pop into our chat room to talk about it, though!)
Having said that, there are a lot of fan theories that are well established and based on extensive examination of the evidence from canon sources. Even though fan theories, by definition, require some speculation, there's a difference (one that's not well defined, unfortunately) between random guessing and informed, reasoned deduction. Theories based on the latter often can generate useful, answerable questions. For example, if you have seen a popular fan theory somewhere else and you don't understand why it makes sense, or what evidence there is to support it, that probably is the kind of question you could ask here.
(As a concrete example, we have a good number of A Song of Ice and Fire questions based on the popular but speculative theory about Jon Snow's parentage.)
If you're genuinely not sure, go ahead and ask. If you make it a clear, well-written question, the worst thing that's likely to happen is it gets closed.
You're asking two different questions here. You can certainly ask questions about fan theories, such as "Has there been speculation about this?", or "Is there any canon evidence for this theory?". But you can't ask questions that don't have verifiable answers, so be sure to phrase your questions so that they can be answered rather than being a springboard for discussion.