2. As an Australian citizen, you have the right to live and work in NZ, and can arrive without any other formalities. However, you need to make the point to INZ that you intend to make your home in NZ, and get your (automatically issued upon arrival) residence visa endorsed with travel conditions. See the paragraph here
http://glossary.immigration.govt.nz/...dresidents.htm starting 'If you intend to stay in New Zealand long term...'
1 and 3. You will be able to sponsor your partner for a partner-sponsored temporary work visa.
http://www.immigration.govt.nz/migra...milystream.htm (You count as a NZ resident.) You will need to provide evidence of partnership, which, for INZ, means living together. See these threads with discussion and examples of what other people have used.
https://www.google.co.uk/#q=site:enz...tnership+proof Overkill on this is GOOD - the more evidence of different kinds you can give, the better. And keep on collecting while the processing is happening, as INZ usually ask for more, just before the visa is issued, so as to be sure they are not giving a visa to someone whose relationship has broken up in the meantime. If you travel ahead of your partner, you will need to collect and show evidence of how you keep up contact to maintain the partnership - phone and skype records, for example, and emails, and any financial transactions between you. Having to be apart should not adversely affect his application, since you can demonstrate the need for you to go because of the job offer, and the need for him to sort out his visa in order to join you.
Later on, you will be able to sponsor him for the partner-sponsored residence visa - you need 12 months' solid evidence for that, and it takes longer to process, so it's probably preferable for you to start with the work visa (which only needs around three months up to the date of application), so he can join you in NZ as soon as possible.
The partner-sponsored work visa is an open visa, which means the holder has the right to live in NZ, and work at any job offered. They don't need to prove any qualifications or work experience.
4. Timings. There is no delay for you. As you'll see here
http://www.immigration.govt.nz/branc...ocessingtimes/, INZ say that most work visas are processed in around a month.