Hi Sternip,
to the forum.
Unfortunately, I'm a bit short of time at the moment to delve into this too deeply, but I would say that whatever you do, if you want to work legally in NZ, you'll need a Work Permit (a Work Visa is if you apply from outside NZ). To get a WP I believe INZ needs to know what salary you would be on and details of the job.
If you are involved with webdesign, do you hold any qualifications that would enable you to apply for Permanent Residency? That would be the easiest way to stay in NZ and, after you got that, you could do whatever you wanted by way of a job. If you could get enough points to apply without a job offer, that would do away with the necessity for you to bring your 'employer' into the matter. It might help that you've had some NZ work experience, but I'm not sure with having been on a WHV, it would count towards your points.
I haven't a clue what a 1015 form is so I can't help on that score and I wouldn't like to say how you'd get around the tax situation unless you started your own business doing the websites and went self-employed or sub-contracted.
Perhaps someone on here has some inside info on this sort of thing and can help out better than I can. I hope you can manage to find your way through this complicated situation.