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Facebook Questions has relaunched as a limited public beta. The limited means it is meant to spread through your personal network: when your Facebook friend asks a question, you can start using the service. The "public" part means that you can bypass that by simply clicking on the green Go to Questions button.
See Emil Protalinski's report, Facebook Questions relaunched as limited public beta.
You're in! After you click on the green button, the text under it will change from "We'll be rolling out Questions to everyone soon, but you can upgrade your account now." to "Your account is already enabled for Questions."