Laura, you might receive more replies if you started a new thread with questions. Anyway, you now have 5 posts, so you might also be able to send personal messages.

The cheapest bike hires I could find were Waikato Car Rentals and Colemans Suzuki.
For a 6-week rental the Canadian couple were sure they wouldn't be stuck with a bike at the end of the trip that they couldn't sell. For longer periods and especially if you're returning to the country, purchasing a bike is probably a better option. There are also some bike dealers who will do a buy-back option if you want to be sure of selling the bike before leaving the country.

Insurance is not compulsory in NZ, but 3rd party insurance is usually cheap and is highly recommended. Included in the registration fee is a contribution to ACC, a compulsory accident compensation scheme for those who are injured in accidents. It does not cover any damage to property.

You could try contacting Star Insurance who have previously covered overseas riders in NZ, to hear what their prices and conditions are. Their email address is on the contact page.

The TradeMe Terms and Conditions for becoming a member has as the first condition:
"Becoming a Member: Becoming a member is free. You may only register as a member if you are resident in New Zealand or Australia and can form a legally binding contract that is enforceable against you. For example, you must be 18 years old. By registering as a member, you warrant that you can form a legally binding contract."

I know someone who lives overseas who has registered as a member, mainly to keep a watchlist of items of interest, but without the possibility of bidding on or buying auction items directly. You can certainly get someone in NZ with a TradeMe account to bid on your behalf.

In NZ anyone without a full motorcycle license is limited to bikes of 250cc or less. So it depends on how the authorities view your Canadian license. A 250cc with low seat height would be a good option for touring and for riding some of the gravel roads that are found in abundance. Unfortunately since all learner riders are limited to 250cc or less these bikes tend to be relatively expensive.