Welcome to FT ahsleyydiego

I presume you have some other way of getting yourselves from SFO to EZE at the start and back home again at the end

The SCL-SYD segment is notoriously difficult to get Economy seats on (in the 'L' booking class that the Oneworld Explorer ticket uses). So you will need to be flexible on that one.
Also, in addition to the Qantas SCL-SYD flight, LAN flies SCL-AKL-SYD. If you could snag seats on SCL-AKL then you could re-jig your South West Pacific visit (NZ first then OZ) and maybe gain an extra segment. Depending on the time of year, Queensland (in the Jun-Sep timeframe) or Western Australia (in the Nov-Mar timeframe) would be good additions

Have you considered breaking the trip in two? Up it to a 5-continent ticket and fly MAD-LAX-LIM; have a break at home before going back to Sth America. You have one year to complete the ticket - from the date of the first flight.

If you use the on-line tool to book, then it will be ticketed by LAN (the first carrier: EZE-SCL). I believe that will result in lower fuel surcharges than booking with other airlines (Qantas is one of the worst)

Earning on AA;:
on QF flights - only 50%
on CX flights 0%
I think 100% on your other main carriers (LA, BA, IB)
Don't know about HG

Happy Planning