Will my Xbox 360 from the UK work when I move to Australia?
Solution 1:
Yes, they should work with your TV, as both the UK and the AUS region use the PAL system, however, be aware that you might need to buy new power cords over there.
As proper broadband uses CAT5 Cables worldwide, a normal plug & play broadband connection should always work. (also, wireless also uses the same basic system worldwide, so no problems there too.)
I sadly wasn't able to find a conclusive answer for this question, however, my tentative guess would be that it is possible.
As far as I know, (and a Google Search seems to agree) prices of games in Australia are more expensive, and with the low £, it might be profitable to stocking up games. (your best bet is to do some price comparison on the games you think on stocking up.)
Be aware however, if you think about trading-in games in Australia that this can be slightly difficult for UK games dependant on Game and Retailer. (luckily no language barrier, just ratings)
Also, be aware of the Australian Censor when Importing Certain Games
Do what you like the best, weither it is gaming or enjoying the climate, just don't overdo it.
(BONUS) Games bought Down Under should usually also work on your system, as both Europe and Australia are usually considered to be in the same zone (related to point 1)
Solution 2:
Regarding point 2:
Your account will work, but you will need to use a UK credit card to buy points and games on demand. There is no way to switch your account to Australia, it will remain a UK account.
Solution 3:
Yes, you will be able to retain your Live account, however, you will have to buy UK Microsoft points cards in order to stock up your account, or retain a UK credit card. Microsoft will not allow you to change the nationality, even when they are at fault (as I found out).