£2 in 1882 was 40/- and there were married men living Chippendale and Darlington who were working for wages of 10/- per diem so their wages over a week would be £3. I can also assure you that 10/- p.d. was going rate for some married men, coal miners in the Hunter district.
Anastasia was the Christian name for the 32 year old patient at the Asylum,
Source : the article mentioned they would exhume the next day. So look for follow up in the newspaper’s edition of the ‘next day’ and find clean copy where it mentions her name.
Christian HENSE in 1878 is clearly shown on the electoral roll as being eligible to be enrolled due to being qualified as having FREEHOLD in Corben Street. In 1882 he is shown as the OWNER/LANDLORD of three properties in that same street, and your Thomas MINTON is his tenant in one of those three. Further, Christian HENSE of that address is listed at Sands as a Music Teacher. So I would suggest that both Thomas MINTON and Christian HENSE would have similar professional standards in respect of music, afterall owning even one property in in Surry Hills was not an opportunity many musicians would have achieved in those decades, and HENSE had three.
Of course, 20 Exeter Place also had an owner/landlord and that was William FLETCHER. Perhaps he was the carrier.
Yes, agree with Cass re cemeteries and burial plots, definitely not individually rated by local government councils. I think you will find that … agh … … in those decades cemeteries were administered by Boards, the members of which were qualified to be Trustees, and the biggest cemetery was at Rookwood, not at Botany.
I am sure that find the parents of Mary MINTON nee MURPHY you need to move away from seeking out Edward Townsend FOLEY and concentrate of Letitia THOMAS nee MURPHY, or perhaps the possibility of a militiary NZ connection via that John FRENCH alias John MURPHY born at Parramatta 1844, afterall, many a child of a soldier was known by his mum's surname rather than his dad's

perhaps the easiest option at present is to save up the pennies and obtain the Vic BDM digitised image of the d.c. for Letitia, as it seems likely it names her parents.
JM on my e-reader. Sorry, cannot do live links to offer sources for above, but I can assure you that Trove will be the secondary source, while my longstanding knowledge of the contents of my family private papers and my decades of research validating much of those records will be my original primary source.