How easy is the kind of work I'd be allowed to do to get? - You can do anything you want but I can almost garuntee your going to end up working in hospitality or a call centre with your degree.

How expensive are living costs and accommodation? Depends where your living. If your in Auckland, $350 might cover 3 weeks rent for a room in a flat. If your in Christchurch you'd probably be able to find a room for $80-$100 a week. Start out in a backpackers and look for a flat on trademe.co.nz

How hard is it to find permanent work and thus get a permanent work visa? Your right in that its going to be very difficult to find anything with your degree. You could find permanent work but fuck knows what it will be.

Most people who do a year here from the UK save as much as they can before they leave, find some fun easy work like in hospo, and work a few months then quit the job and move to another city or spend a few months travelling and repeat and see as much of the country as you can inbetween.