You could insure the car under your parent's name, however, there's one downside to this and that's that you won't be developing a no claim bonus for yourself, therefore it's not the best thing to do in the long run. As far as companies to insure you go, Famous Classic Car Insuance is probrably your best bet. Try searching the New South Wales forum for the Insurance threads, as there's more companies and things listed there. Insurance is always going to be high when you're young, and drive a turbo imported sports coupe.
Try using the Search feature on the forums to shed more light on this subject of what to look out for, there's been threads on this before and it so it could be of some help to you. Basically, look out for leaks around the engine block, noisy/smokey turbos, rough idle, blue smoke, and stuff like that as far as the engine goes. You should take it for a test drive of course, check the gearbox is alright and the clutch isn't slipping. As i said, use the search feature to find more information on what you should look for on R33's. Your best bet is probrably finding a near stock example; you're likely to have less problems with it as there's less chance of it being thrashed/used for racing/drifting etc. If you can find one with Japanese log books, this is great. Sure you can't read them, but it's reassurance that it's been looked after and serviced by previous owners.
Looks promising, looks pretty neat too. 12 months rego - Bonus. Try haggle him down a lil ($500-750?) and you've got yourself a good deal IMO.
I think you'd have more fun with the Manual, however, if you're more comfortable with an Auto go ahead with it. Manual would be better though, especially if you intend on adding performance mods in the future. Manual lessons are good, you'll get the hang of it. Though, in the end, it's your money and your car - get what transmission you're comfortable with. You won't find an Auto as easily as you will Manual, as the Manual's are more common, though.
Hope that helps you a little.