What is the relationship between the dryness of a plant's root and the healing of a sciatica patient, and is it permissible to seek treatment from a person who uses this method, knowing that he is a muezzin in a mosque?

This method is not derived from the Sharia, nor is there anything in reason, custom, or sense that indicates it. What is like that is not permissible to do, nor is it permissible to believe that it is a cause. The fact that the doer of that works as a muezzin does not indicate the correctness of his action, for the actions of individual accountable persons are not to be used as evidence.