Looking to book a J RTW OW ticket through AA. WHEN it is booked through AA, can you still use AA but not OW partners like TN, or OW connect airlines? Basically, I am trying to book something like:

JFK-DOH-SGN-TYO-HKG-SYD-AKL-???-PPT-IPC-SCL-JFK

I am wondering:
1. Can I can use TN between AKL and PPT?
2. If there a way to use FJ through NAN as a OW connect partner to get between AKL and PPT?
3. If I took NZ to PPT, is it possible to have an open jaw or "overland" segment gap between AKL and PPT on a OW RTW itin?

Looking to book this fairly soon. Thanks!