Is lying on websites that issue fatwas—by using a pseudonym or another email address—considered lying against Allah and His Messenger, and can that lead to disbelief?

Using a pseudonym when creating an email account is permissible and does not constitute disbelief (kufr). No one has equated lying about scholars with lying about Allah and His Messenger (peace be upon him), nor has anyone declared someone a disbeliever merely for lying about scholars. This is because there is a specific stern warning regarding lying about the Prophet (peace be upon him): "Indeed, a lie about me is not like a lie about anyone else. Whoever intentionally lies about me shall take his place in the Hellfire." The questioner is advised to disregard such whispers (waswasah).