There is a 'Criteria' tab on this factsheet that tells you what is required.
https://www.immigration.govt.nz/new-...work-visa-open There is a bit more detail here.
http://onlineservices.immigration.go...nual/index.htm
Your question 2. As it says on that page you have quoted,
https://www.immigration.govt.nz/new-...e-of-my-papers, you need to provide some evidence from your course provider that - to put it bluntly - shows it is worth giving you more time to complete your qualification. If a person has a bad attendance record leading to very little progress, for instance, they won't get permission to stay longer in NZ.
3. You need to get in touch with INZ to see what you can legally do at this late stage. You have left things very late.
By the way, a visitor's visa is not just a catch-all for people who don't qualify for any other visa for the time being (unless INZ themselves decide to grant one as a temporary measure). If you apply for a visitor's visa, it genuinely means that you intend to make a short stay in NZ that will come to an end, and you will then leave and go back to another life in another country. You are not wanting to do this, which is obvious by the way you are trying to get a different visa, so INZ could say applying for a visitor's visa is fraud.