Does Facebook provide a way to only search questions?
Facebook do not currently allow search engines to index any questions or answers of their Questions product; thus, there is no way to search for questions. There is also no way to search for questions through any of Facebook's interfaces (mobile, web etc.)
Facebook have designed Questions so that each question will become discoverable to people when they see their friends vote or answer; that is the only way questions can currently spread or be found.
ChrisF's earlier suggestion does not work, due to what I have explained above about the lack of indexing. Here is an example: http://www.google.co.uk/search?sclient=psy&hl=en&site=&source=hp&q=Charlie+Sheen+site:www.facebook.com%2Fquestions&aq=f&aqi=&aql=&oq=&pbx=1&cad=cbv
If you append
I know this works for Google and Bing, so I expect it will work for most (if not all) other search engines.