Air New Zealand Insurance covers the following occurrences, as per their website:
Terrorism and extreme weather events: travelling to specific regions against the advice of the government or your insurer may result in unsuccessful claims because the events are no longer unforeseeable circumstances.
Yes - Airpoints dollars can cover a number of things, including travel insurance.
Yes - If you're not sure about your policy, you can cancel within 15 working days and get a full refund.
Yes - Air New Zealand contracts through Cover-More for its travel insurance.