You qualify by virtue of having an international ticket that bookends the domestics, irrespective of how long you stopover. Basically if you have an international ticket... (that can be train, ferry, cruise, flights...),, you're covered,
For more expensive domestic fares, you can exempt two taxes on the domestic ticket if you also have an international ticket.
You have to purchase from a travel agent that knows how to do tax exemptions and they must be located outside of the US though, but in your example you could probably get...
For QF direct bookings, if your ticket was worth $500 and you book a new fare that is lower, eg. $200, then the $200 fare will use the existing PNR and a new PNR will be created for the remaining $300 credit.
For agency bookings... you can just re-use the same PNR over and over.
I have seen this incorrect information being sprouted for quite some time now... so for the sake of getting it right...
For QF flights, QF sets the fuel surcharge. You are correct that these go to QF's bottom line. However, for non-QF flights, QF doesn't set the fuel surcharge at all.
Carriers...
If you know your passports are already linked (the link lasts for the life of the foreign passport, even if you get a new AUS passport the links are automatically carried over), never hand over both passports, only the one you will enter the destination with.
The fact you had to use the AUS...
The correct process is you use the passport you checked in with in the smartgate, so that means you use the USA passport in the smartgate, not the AUS passport.
Something is not adding up here... SQ is probably the only major carrier who does very few schedule changes and certainly cancelling flights altogether is not something that SQ does often. So why were the flights cancelled?
In that case, don't check in online at all. At MAD, show them both passports. They will need to swipe the USA passport which will give you a boarding pass to DFW, then at DFW give QF the AUS passport to get the DFW-MEL boarding pass.
This has been ongoing for a while now across a number of carriers... the ones that I'm aware of are QF, AC, SQ, QR ... possibly others. Essentially they pinch the booking reference/pax name and then go and change the FF number to a newly created FF account in the pax's name, then they steal...
For CGK/NYC or CGK/PHL, yes, 1280 TPs at 5200 AUD is the maximum TPs possible.
If you're purely after TPs, the KUL/LAX fare is better value where the maximum is 1440 TPs for about 5500 AUD.
This AA fare, along with the KUL/LAX fare, never goes on sale. Neither fare has gone on sale at all in the past 12 months. Any difference in pricing will purely be differences in availability.
The CGK/NYC or CGK/PHL R class version is about 4400 AUD currently, and the C class version which is...