1) NRT-AKL-ZQN: you can't check your bag though onto a domestic flight, all baggage has to be collected at the International arrival port, then you have to take it though full customs and quarantine screening. Its very unlikely that they will allow you to check-in your bags in AKL as your flight departs on a different day.

2) CHC-WLG-SYD: The system wont allow to check-in your bags to SYD, as your departing on an different day to your arrival.

NZ's check-in is all full automated at AKL/CHC/WLG e.g they removed the check-in counters. The machines will only print bag tags for same day connections / and only 2 hours before an domestic flight. In saying that it only takes 60 seconds, includeing dropping your bags.