Is the Mahdi not Arab because he will emerge from Khurasan, and do people from the Household of the Prophet (Ahl al-Bayt), descendants of Fatimah, live in Khurasan now?

We have not found any authentic hadith indicating that Imam Mahdi will emerge from Khorasan. Rather, the authentic hadiths indicate that Dajjal is the one who will emerge from a land in the East called Khorasan. Even if that were to be established in an authentic hadith, it would not necessarily mean that the Mahdi is not an Arab, for Arabs may settle in any place.