Are exempted fast tags work in the entire india? Or only in issuing state? If only in one state, how can I travel in other states?

The rule is different for different categories of FASTag. For example:- an exempted category FASTag issued to a MLA will only work in his state whereas an MP will be issued two tags one will work inter-state only and one will work pan India. Kindly check the corrigendum issued by NHAI for further reference.