Is anyone commuting from AKL or South Island, NZ?
With ANA not going to AKL, would the 2,000$ travel allowance be your only option then (and not a confirmed C class)?
Commuting to NZ is not a snag and, surprisingly 
they've even allowed a few Kiwis to join the AJX gang. When they organise your commuting they'll use ANA if they can. If ANA does not serve that destination, they'll use Star Alliance carriers. After that they'll use others they have lesser agreements with e.g. Qantas. So C Class commuting IS still available, even though ANA don't fly to AKL. I believe Air NZ offer a direct flight NRT-AKL but I also know that sometimes guys route via SYD. That may have something to do with direct flights not being available every day (I don't know the reason for sure) but, if that is the case then C Class is still available; you'd just do something like QF NRT-SYD and then either QF or Air NZ SYD-AKL. Long and short of it is C Class commuting is no problem to NZ.
(a little off topic here...)
Have any commuters (foreign to the USA), managed to gain residency in the USA and commute from there? (i.e. proving that you have income, and don't need a work VISA - just residency). (Something that I'm trying to research at the moment).
Can't help on that one 
Another one:
My wife is from Europe: is it possible to change commuting destinations periodically (in advance) if you need to go to another continent for your home leave?
You can register 2 'home' addresses when you join. There are a few guys who have family on different continents and do exactly as you want to do i.e. travel to Europe during your days off, rather than NZ.I believe they were looking into how often you could change your 2nd address but, so far, I haven't heard anything about it and think you can change it quite often. For your case, though, it's not a problem having your NZ address and a European address registered for commuting purposes (and, yes, C Class does apply to both).