I would directly contact the university or polytech you are interested in.
NZ nurses do their Bachelor of Nursing straight after graduation from high school. There is no need to do prerequisites. The BN programme in NZ is 3 years long.
I thik NZ education is cheaper than in the US but as a non-resident, and I'm presuming you are, you will not be eligible for government subsidies or loans and will need to pay the fees upfront, if and when you are interested.
On a student visa you are allowed to work a maximum of twenty hours per week unless it is semester break then you can work however many hours you wish.
The cost of living is high in most places, especially food. You will have to factor that in when making a decision. As a nurse with 10 years experience I was earning $32 per hour basic pay, but after weekend and shift differentials I ended up earning more than $NZ80,000 last financial year of which $21,000 was taken out in taxes (so left me with roughly 6
$60,000+). My rent was $1,560/month for a very tiny studio in Auckland. At the end of the day, it is not bad. NZ has an excellent healthcare system that is totally free for residents and citizens, so you don't have to pay for health insurance.
The working conditions are so worker friendly. Kiwis love their work-life balance and I got so used to it that when I moved to the US I was appalled at the working conditions here. Kiwis get a minimum of 4 weeks annual leave, an additional 1 week if you work shifts. The weekend penalty rates are 150%, night and afternoon shifts 125%, public holidays 200%. On my 12 hour shifts I got three (yes three!) 30-minute breaks (here in the US I get one 30-minute break and one 15-minute break). The nurses union is powerful and there is no culture of frivolous litigation like in the US (unless you are negligent of course).
I had the time of my life living there for 5 years. I enjoyed every single corner of the country I explored and if only my family and friends lived there I would've stayed for good (not to say I didn't make any close friends,I did). New Zealand is a beautiful country and it will all be worth it.
I wish you luck!