From what date did they have to pay them? Did they have to pay royalties dating back from their first recordings? Or only after the purchase?

My understanding is that payment to Folkways for the royalties from the piece used by Men At Work has the starting date of 2002. I'm not sure but I suspect this is when Folkways first noticed the "unauthorised" use of material to which they had copyright and requested recompense from M@W.

What is the South Australian State library doing selling off State Property to the highest bidder?

Owners of commodities have the right to dispose of them by approved methods. You and I might not regard such things as commodities but govt institutions that are strapped for cash obviously do.

To answer your question about Robbie Burns' material, check the details in various postings earlier in the thread for different jurisdictions' treatments. Many other Mudcat threads have authoritative comments on such matters, as well.

Cheers, Rowan