Unless you have family in the UK you can't jump from a working holiday visa to British citizenship, but you could apply for permanent residency and then apply for citizenship after you have been in the UK for a while. This is really a question for an immigration lawyer, but it helps if you have an occupation that is in demand in the UK, or if you're self employed or marry a British citizen. Just take it one step at a time.
It shouldn't take much longer than a week to find a job. Make appointments to see all the big temp agencies before you arrive so you have your job interviews already sorted.
Most Aussie backpackers live in the suburbs in West London, usually around Acton, Hammersmith, Earls Court and Willesden. Earls Court is more central but costs more (because it is right next to posh Kensington), but Acton and Willesden are cheaper. East London is cheaper but it is harder to find a house to share with a bunch of other backpackers. Rent in London is really expensive, but most other things aren't too bad.
It is easier to open an account with HSBC, but you need a huge opening deposit and the fees to open the account are high. If you sort out as much documentation as possible in advance you should be able to open an account with another bank when you arrive but it will be difficult to prove your UK address without having friends over there to help you out. You need to get a letter of introduction from your bank manager in Australia as well as utility bills with a British address to show that you live there. If you know people in the UK you can sort this out in advance (just get them to change the name on their cable or broadband bill for a couple of months). It is a lot easier to open an account with a smaller bank like Abbey, especially if it is a branch away from the popular backpacker haunts like Bayswater, Acton or Earls Court. An alternative is to use the services of a company like
www.1stcontact.co.uk who can fast track your bank account applications.
Yes, you can drive for a year on an Australian licence. After that you can exchange it for a British licence (I think the fee is £21), which doesn't expire until you're 65.