Are the Bandwidth authorities and the Directory Authorities the same servers? do the same people run both? or am i posing the wrong question, is reporting on bandwidth a job that the Directory authorities perform?
A bandwidth authority is just a directory authority that also measures relays and votes about their speeds.
The code that performs the measurements is usually run by the same person as the actual tor process that is a directory authority, but it doesn't have to be.
The measurements do not have to be performed on the same machine as the tor process that is a directory authority.