I can't say that I even realized Facebook had a separate application that launched a few years ago called Facebook Questions. The only question service that I knew on the social network, which is still available, are the questions that you can ask via your Facebook status box. Facebook Questions became available to all Facebook users in March 2011 (launched in June 2010 initially) at facebook.com/questions.
The idea was that Facebook Questions was placed users to go to ask questions that could be seen by all Facebook users and even search engines. The idea was that rather than opening your questions up to your friends list alone, you ask the question of everyone to get quick and accurate answers. The URLs that used to go to Facebook Questions now go to pages where the Questions app is no longer listed.
Facebook didn't even bother to announce that Questions had been killed. Presumably, that means that there were so few users Facebook just didn't bother. It's unclear exactly when the service was discontinued. The service was originally aimed to compete against similar offerings online, including Yahoo Answers.
According to Marketingland.com, the only official response from Yahoo on what happened to Questions is "We're looking into it." You can still post questions to your friends list; those questions follow your individual privacy settings.