Can't help with the AD specific questions but....
Cars - loans of up to 250,000 dirhams are generally available. That would get you something both good AND flash. There's a wide choice and no sales tax. Some brands are cheaper in the UAE than elsewhere, but prices are fashion-dependent. Thus, BMWs are expensive compared with the USA, yet American Fords and Australian GMs are relatively good value. Check out
Drive Arabia - Dubai Live - UAE, Saudi, Kuwait, Oman, Qatar, Bahrain and GCC for prices and some road tests.
Be aware that insurance rates are doubled for anything with 2 doors, and bring some evidence of no-claims discount/bonus from your previous insurer.
Many people end up with SUVs even if they don't intend to drive in the desert, partly for reasons of fashion and often because of the perceived safety of driving a tank among drivers of questionable judgement and talent.
Phones/net - not sure about costs of phoning Australia. However, many people break the law and use Skype to phone overseas. Skype cannot be downloaded in the UAE or used to phone a landline from the UAE without a VPN, and UAE credit cards cannot be used to buy Skype credit (so I'm told...). Our complete package of TV (movies but not sports channels), 2Mb internet and home phone costs about 800 dirhams a month, not including the cost of long distance and international calls.
Bring/don't bring - the electricity supply is 220V/50Hz. Generally, it's not worth bringing appliances unless you're really attached to them. My other half's Kitchenaid food mixer came with us, and we run it through a transformer. Transformers are cheap and plentiful, but possibly not the best thing for really pricey electronics. Multi-region DVD players are available here (as are pirated DVDs...), and TVs are similar to US prices. If you have expensive stereo equipment, it might be worth bringing as the more esoteric makers aren't sold here, or are sold here at a premium.
Other household items, beds, furniture, etc, really depend on whether you're attached enough to them to pay the shipping costs. The fact that you may have to wait three months for a shipment tends to force you into buying furniture here anyway.
Have a look at
BetterHomes for villas and flats. Rental costs in Dubai have decreased markedly in the downturn, though I'm not sure the same if true of Abu Dhabi which was more expensive to begin with.