I've been to Adelaide before and it's a beautiful city, though I was there for work and didn't get to see much 
I've never done the drive you want to do. The closest I've gotten is going on the Indian Pacific from Sydney to Perth with my grandmother when I was a teenager, and having been in inland NSW a few times where it's flat and not much traffic, that trip put a whole new context on the word vast. There was nothing but flatness going as far as the eye can see for days, and I remember getting excited when I saw a junked out car on the side of the tracks at one point, coz I got really bored really quickly with the nothingness.
That's a really long drive yr wanting to do, but I'd be thinking you could do it comfortably in 3 weeks. It's just over 3000km and a lot of it's the Stuart Highway, which should be a pretty comfortable drive. I don't know if you've found something like this already, but this site probably has a lot of useful information on roads and trips and stuff.
http://www.mynrma.com.au/trip-planner.htm
I'd get a campervan. Well I would if I were you, but I'm a 5 star accommodation girl so I wouldn't if it were me 
http://www.vroomvroomvroom.com.au/campervans/
If yr going off the beaten track, be mindful of any restrictions the hire company has on what roads you can't drive on. I hired a car in NZ and found there were a few places like the road to Milford Sound where they advised hire cars not to go coz the road's too dangerous. And don't go too far off the beaten track and get yrself lost. Getting lost out that way can be really dangerous.
Food? I can answer that with some authority coz my brother went to the US year before last and had a lot to say about it. He thought food was a bit cheaper here, but that beef and lamb was amazingly cheaper here than there. Also, the servings in restaurants will be smaller than in the US. He said they had massive servings over there and one place he went to had no idea what a doggy bag was. And we don't tip here. They pay good wages to hospitality staff, at least they do now but Tony Abbott would like to change that.
As for gifts, I'm no help. One of my friends brought me back a really cute Obama bobble-head doll from Hawaii that was Made In China, but while I loved it, I'm not sure if anyone else would.
I'm nowhere near where yr going. If you were in Sydney, I'd catch the bus up from Canberra and have a mini DU meet-up for sure 
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