-Do a search on here, plenty have asked about it
-Do a search for Australian lawyers in Auckland (google), get the countersigning done for *free* if you ask nicely
-You can get an AVID much quicker than a ASIC, and get the licence issued on that basis. But yes you will need a ASIC for when actually in a job there, though you might be able to pass that cost off to the new employer!!??
-Initial issue Australian medical requirement is satisfied by your current NZ medical. When that expires you will then need an Australian medical certificate.
The casa website has all the details of who they recognise around the world for the doc and eyes etc.