1. See this INZ fact sheet.
https://www.immigration.govt.nz/new-...-visa#criteria If either one of them meets the criteria, s/he can apply for the visa, with the partner as secondary applicant, and both can get a visa. BUT BE AWARE, unless the person who is the main applicant has a skilled job offer in New Zealand, or a higher degree gained in New Zealand, they can only in the first place be offered a Skilled Migrant Category Job Search Visa. This entitles the main applicant to be in NZ for up to 9 months to secure the offer of a skilled job: when they can show the offer and the contract, INZ will then issue the residence visa that has been waiting for them, AND for the secondary applicant.
2. Here
https://www.immigration.govt.nz/new-...lders#criteria is the fact sheet about the visa for your partner. It does not give a timing in the criteria, but we know from experience that INZ take applications seriously with around three months'-worth of evidence of living together. Here
https://www.google.co.uk/search?sour....0.812SSOWD_68 are old threads with discussion and examples of evidence of partnership.