1. Is there a clear definition of money supply as defined by the Austrian school and if so what is it ?
I have seen one defintion here :
and an argument against it, here:
Do we have a consensus on this ?
2. Assuming we can clearly define it, how do we compute that from M1, M2, M3 and MZM data ? I am trying to figure out inflation (the monetary inflation according to Austrian school) from these data.
A good start might be Rothbard's America's Great Depression. This topic is not my strong point, but he is at some length to argue how to define what money is and how to count it. Of course, he is using data from decades ago and things might have changed. Like I said, it could be a good place to start.
As for M1 and the rest, each one is contained in the M of the next highest number. That's about all I can tell you.
Every decent man is ashamed of the government he lives under - Mencken