Hi Katja,
Air NZ uses the standard IATA SSR codes for disabled passengers, such as you've already posted in the 'BA' section of the sticky, with the exception of 'SMED' which I don't believe is used by NZ at all.
I think WCHC passengers are assigned certain rows (these are the only seats where the armrests lift fully up on the 747/777 aircraft).
I also believe that dogs are the only assistance animals allowed in the cabin.
Hope this helps!