You mean with Amazon Instant Video?
It will load within your account and then you need to watch it through Amazon's Instant Video app/website/program - depending on where you are accessing the account.
As long as you "buy" it and don't "rent" it you can watch it as many times as you like and it will stay in your Amazon account for you to click and watch as and when you wish - there is no expiry.
Time for the legal bit...in the terms & conditions you agree to with Amazon you wont be able to burn it to DVD. Amazon uses DRM protection on its shows/movies. So while you can download and burn the movie to DVD you cant then watch it from the DVD [its not actually compatible] - the burned DVD is designed to just be used as a back up and watched again through Amazon Instant Video. For more information on DRM please pm Cat direct
Yes it will affect your bandwidth as typically you will be streaming the show - it does not download to your computer but simply sits in the cloud for you to access as and when and where you wish. So each time you watch it you use bandwidth. HD content can be a monster when streaming - so make sure you have a super fast connection and are prepared for your bandwidth to be hogged if you are not on fibre optic.
Also - make sure it will play in NZ. Depending on which Amazon you are buying from sometimes you have to get clever with your settings to ensure you can watch things.
Also weird question - but do you have an XBox 360 or a Wii or something similar? Both of them carry Amazon Instant Video channels/apps which will allow you to watch it on the television you have the games console hooked up to. Thats assuming your television or cable/satellite provider is not internet ready already.