Hi Mao

There's no direct OW flight from BKK-AKL [though you could route this via HKG and pick up a CX direct flight from there; otherwise it's QF/BA to SYD/MEL and a QF connecting flight on from there].

South America is where you come unstuck as this is where you're reliant on the services of Lan Chile and Lan Peru. Suggest you take a look at the respective route maps of each [most flights outside of Chile and Peru will involve a routing via SCL or LIM].

You can go back to SCL as many times as you wish within the 4 included sectors, but anything longer than 24 hours will be regarded as a stopover. You also need to watch those sectors adding up: UIO-CCS for instance will involve using LA and connecting in SCL or AA via Miami.

Given that the bulk of your travelling is in S America you may find it more advantageous to buy a Visit South America pass to use in conjunction with your MONE, though I defer to others on this board as to whether it's permissible to do so.

Have a great trip.