Can I ask a couple of questions about diversion airports?
Do you know which airports are used in the event of a late requirement to divert from JNB, SCL and LAX (eg. airfield closed unexpectedly)? I appreciate the airports have multiple runways so eg. in the event of an aircraft blocking the preferred runway they could use an alternate but I guess the situation could arise whereby the whole airfied was closed (unexpectedly) - I'm not meaning eg. predicted weather / storms. I assume there are multiple options but there are pros and cons to each?
You have to accept that on many occasions, there comes a point at which you have no diversion options. Yes, there might be a runway nearby that you could use in a pinch (i.e. Avalon, Richmond, Ontario), but in some cases the destination is the only option that is big enough, and for which you have fuel. You don't, as a matter of course, carry a diversion all the way to destination. As a last option, max braking, and the longest section of runway available. I expect you'd be surprised at how quickly you can stop if you're not concerned about brake temperature, or passenger comfort.
If the DFW-SYD (or the old DFW-BNE) flight had a planned stop in eg. NOU is the aircraft fuelled to an amount appropriate for a plan to stop in NOU (and thus a "maximum" refuel in NOU) or will it carry "extra" to minimise the amount of fuel needed to be taken on in NOU?
It can't have a planned stop like that, as it would almost certainly exceed the planned crew duty limits. As there's obviously plenty of warning to plan such an operation, you'd also have plenty of time to put a replacement crew on station. In that case, Brisbane is the most likely place to go. Last time I saw a similar operation, it was LA to Melbourne, and they placed a replacement crew in Auckland. Total ground time was about 40 minutes.
Fuel loading...sometimes we tanker fuel, but in most cases we'd simply carry what was needed for the sector. With a planned stop, you'd be better off carrying a bit extra on the first sector, and burning it by going as fast as possible. Extra fuel, means extra weigh when landing, and so extra brake temperature. Not all places have facilities to cool the brakes, so if they got hot on the landing, that could delay the departure.