RE. New Zealand
I remember contacting airways a couple of years ago when they had an advert in flight and came across a catch 22 situation they won't employ you without new zealand residency and New zealand residency won't be granted unless you have a job offer.
.
ATC isn't a priorty job in NZ immigration policy at present so even I a native english speaker with cousin's and other relatives in NZ would struggle to get residency, I'd have more chance if I said I was an entrepeneur.
I didn't pursue it any further as the salary they quoted for an aerodrome/approach controller worked out at less than what i was earning and the wife wasn't keen.