If you are shipping stuff out and like IKEA style then I agree go there and get before you go. Otherwise there are loads of bed places here - just bought DD1 a double sized from Brownies, was quite reasonable, and NZ made.
Yes there are furniture rental companies, also furinished flats (although not large numbers).
They're changing the rules to make it harder to import second hand cars from 1 Jan next year which will push up the price of all imported cars. Toyota is generally held out as the most reliable brand and cheapest overall to run, but Honda, Mazda etc fine too.
I wouldn't go through LAX if you paid me, world's worst airport, horrible people, generally a bad experience every time. However it is the most direct if you fly NZ1 all the way from London to Akld in one go. Singapore is hot and sterile with good food. HK is mad and busy but also has great food and shopping (and Disneyland).