It seems there is some confusion here. AAalot, on the Global Explorer, you are limited in miles but you can use a lot of other carriers that you cannot use in the other Oneworld products. That's why you can't do your trip as a Circle Pacific.

So assuming youre doing a Global Explorer, you can use the following airlines under their own designator.

British Airways
Qantas
American Airlines
Aer Lingus
Lan Chile
Finnair
Iberia
Cathay Pacific
Gulf Air
Lan Peru
Air Pacific
Swiss Air

Codeshares are a bit more complicated but can be summed up in two rules.

First, you can book any codeshare that exists within the aforementioned group. So you can book an American Airlines codeshare with Cathay or a Finnair codeshare with BA, and etc.

Second, you can book codeshares on Qantas on any of the following airlines:
Air Vanuatu
Air Tahiti Nui
Air Nuigini
South African Air
Air Caladonie
Vietnam Airlines

Those flights *must* be on a Qantas designator and can *not* be on the originating airlines designator. In other words, if you want to book AKL-PPT you *must* book QF3825 and cannot book TN102

Now for your other questions, yes you can backtrack within the same "continent" with limited exceptions that don't apply here (such as not through your contry of origin or your city of origin).

Youre allowed as many segments as you want in any single continent as long as the total does not go over 20 and youre not flying the same segment more than once.

Youre limited to 15 stopovers total and 4 per continent. Your continent of origin (North America) youre limited to only two.

You can do a surface but must accout for the mileage in the total.

You proposed (stopovers in parens):
TVC-ORD-LAX-AKL-(CHC)-AKL-(PPT)-(AKL//SYD)-BKK-LHR-(ORD)-(DFW)-ORD-TVC

So your stops are:
Christchurch
Papeete
Auckland/Sydney
Chicago
Dallas

Total mileage is about 32000 miles

Both are well within your allotments.

Now. Suggestions and tips. First, you can add the AKL-SYD segment without hurting anything. Second, you can also add stops in Asia and Europe if you choose. Finally, the AKL-PPT-AKL must be booked on a QF flight designator. The others you can book on the operating flight designator.