It depends........
a) If he is considered a legal resident of Australia during his stay in that country, he will be subject to Australian tax? Australia taxes its tax payers on their world wide income. If he is performing the work for the US company while he is treated as a resident of Australia, his US income would be taxable in Australia
b) If he remains a UK tax resident, both the Australian and the US income would be taxed in the UK. You need to research about double tax agreements and foreign tax credits in the UK.
c) He is not subject to income tax in the US provided that he qualifies as an independent Contractor and not an Employee. The acid test for that is how the contract is worded and the relationship handled. To qualify as a Independent Contractor, the company for whom he works can exercise control over his work but cannot define the location nor the time when and where the work will be done. He must be truly independent.
c) I think the question about the bank accounts depends mainly on his personal financial situation during the time he lives in Australia.
d) and finally, do not forget that there will be 3 currencies involved. And as such, all of them are subject to changes in their values.