For visa purposes, an 'eligible New Zealand citizen' is a person who resided in Australia prior to 26th February 2001 holding a Special Category Visa (444); or lived in Australia for at least one year in the two years preceding 26th February 2001; or has a certificate, issued under the Social Security Act in 1991, that states that the New Zealand citizen was residing in Australia on a particular date.

Only under the visa category of Sponsored New Zealand Family Member, which is a temporary 5 year visa that can be renewed.

No, you have first become an Australian Permanent resident before you can apply for Citizenship.

You have to apply for a permanent resident visa from one of the available categories.