Certainly not a tax expert…but I do believe you would need to pay your local host tax, then you would file your US tax (excluding the first 100K), whatever you owed to US would be offset by your host tax.
As far as Australia, the way it was explained to me was I would get a working visa and not be considered as a resident. Residents had stepped up tax rates, but as a non resident they would tax me at a higher rate on my total pay.
When I was an expat at another country, I declared NJ as my resident, so my company also paid for my state taxes. D2 was able to participate in a NJ sponsored summer program and she would have been able to go to a NJ state school.
Yes, there is a residence test that one can use to qualify for the foreign income exclusion. That’s the 330 day test.