What does a broker cost me?
Brokers are usually paid commission by the insurer, sometimes with a fee on top for commercial work. Ask which applies and whether any fee is charged to you, because the answer should be plain.
Broker or buy direct?
Direct is often fine for a straightforward car or contents policy. A broker earns their place on business cover, trades liability and anything where the exclusions are what matter.
What is sum insured, and why do they keep asking?
Most New Zealand house policies are sum insured rather than full replacement, so the figure you nominate is the cap. Getting it wrong is the most common way people find themselves underinsured after a loss.
Will they help if I have to claim?
That is the main practical reason to use one. Ask directly how they handle claims, since it is the moment the relationship is worth something.