As for other operators ops in the country, its in the CAO's or CAR's somewhere. Perfectly legal since 1988!
I think you may be getting confused here. Yes, Australia and New Zealand have an agreement recognizing each other's licencing standards and enabling the operation of ZK- registered aircraft in Australia, or VH- registered aircraft in NZ. However, the operation of other foreign registered aircraft requires that
- they be registered in an ICAO contracting state
- the aircraft may operate from, but not within, Australia
- the operator hold an Australian foreign operator's AOC
With NZ registered aircraft, CASA have a degree of control via their agreements with CAA NZ. With aircraft registered elsewhere they do not.