My degree is in Math, and I don't recall any problems with getting bonus points for being a programmer. I don't remember the exact rules, though -- isn't it something like you need a degree *or* a certain number of years of experience?
If your "real" application drops you below the number of points that were needed to be selected from the pool (at the time your application was selected -- not the current threshold), then I believe your application will go back into the pool.
There is no requirement to get a job in the same field that you get bonus points in. The idea behind the bonus points is that it gives NZIS additional confidence that you will be able to find a job, since the bonus point occupations are in demand.
I would recommend option #3 -- get a job offer from an employer in NZ. That's the cleanest, fastest, surest way of getting accepted. Although I didn't need the points, it's also what I ended up doing. Since you only need to work for 3 months for the company that hires you, getting a job is easier than most people seem to think. The trick, if you can swing it financially, is to not care what you get paid, and to let your potential employer know that. If you're willing to work for a big discount to market prices, it's usually very easy to find work. That can also give you flexibility in terms of where you want to live.
Then, once you arrive, you can start looking for a new / better / ideal job at a better wage, and after 3 months, make the change.
One thing to keep in mind with option #3, though, is that you have to start your new job within 3 months of when you first arrive in NZ -- whereas if you don't have an offer up-front, you have a lot longer to get everything figured out.
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