What is a Muslim teacher called?

Answer 1

A Sufi (soo-fee).

There is no consistent term for Islamic teachers. The Sufis are the Islamic equivalent of Monks and live generally as holy men. Some are teachers, but most are not, save to other Sufis. There are the Ulemaa (single is Alem) who are religious scholars, but again they do not often teach, but decide theoretical issues and arbitrate disputes. There are the Mu'alimin who will guide Muslims in practice and observance, serving as cultural guides, but they usually do not teach in a traditional western sense. Finally, there are the Usatedha (single is Ustadh) who are closer to the Western conception of a professor.