The spider in the second image is an orb weaver (family Araneidae). There are about three dozen species of these in New Zealand – see The Spiders of New Zealand. Part VI. Otago Museum Bulletin No. 6, Dunedin, pp. 68-124), but online images do not appear available for many of these.
The spiders in images three and four are jumping spiders (family Salticidae); some 200 species of these are believed to occur on New Zealand. Although the one eating the moth could be in the genus Helpis (see http://www.flickr.com/photos/robertwhyte/5429204066/ for an example), only a small fraction of New Zealand’s jumping spiders have been properly described and I would hesitate to say any more.