This still doesn't work. PPT is in SWP not S America. As stated above you can only go to PPT if you then use a separate ticket (on Air Tahiti Nui I guess) to get to Aus or NZ.

Moreover, you can't do SYD-PER-SYD. Only one "transcon" is allowed in Australia, but you do have free segments, so you could do SYD-PER-DRW-SYD. Why not also go to AKL then get more time on CX on AKL-HKG?

CAI-MAD-SCL-UIO//LIM-SCL-PPT//SYD-PER-DRW-SYD-AKL-HKG-DPS-HKG-CMB//HKG--NRT-LHR-DXB-LHR-MOW//MAD-CAI

I don't understand your question on dates... if the flight schedule fits then you would need to check with a Travel Agent or the airlines for availability in A class on those dates.