An ARC DECRA does go to your own bank account as it pays your salary.
Btw, as an Australian you can't apply for a NSF fellowship nor a European fellowship.
You can apply for European fellowships if you reside within Europe, same rule that goes for Europeans living in Australia. See for example the rules for DFG funding in Germany: http://www.dfg.de/en/research_funding/programmes/individual/...
>Eligibility:
> International researchers from all disciplines who have completed their scientific training (doctorate)
And from my understanding that is what replacement 457 will ensure.
"A DECRA Recipient may be awarded ARC funding of up to $139,369 per year of funding. The per annum salary contribution from the ARC is fixed at $99,369 (2016$), including 30 per cent on-costs, and up to a maximum of $40,000 project costs." - From ARC funding rules for DECRA.
So basically, close to $100K per annum goes to you (pre-tax) for 3 years and $30K to the university per annum. For project costs it depends on how you spend them.