Question 5: Firstly, you can just but in dummy dates. Those can then be changed free of charge later. The other possibility is to book some segments as open segments. This means it will say LHR-MIA in the ticket but doesn't state date, airline or flight number. This will be confirmed later.
In general it is advisable to look flights in as early as possible especially in Economy. The reason for this is that economy books into a very low booking class which sells out early on some routes.

Question 6: Yes this look okay. In addition to what malcolmkettering has said, the MEX-JFK flight is actually not coming up in the OW tool (just the codeshare). I have put it into my proposal for you because I assumed that by the time you ticket the flight will be available.
By starting in Australia, you obviously free up 2 segments which you can use elsewhere. But you will pay a few hundred $$$ more for this privilege so you need to do the math to see whether it is better to start in NZ and buy an separate ticket or start in Australia and pay a higher price. And you need money to go to Australia when you are in NZ anyway.


Questions 7: Actually, there is one other way: CX flies from HKG to South Africa. But this is not really helpful in your case I guess. Unless you change other things.

Questions 8: Actually, getting around in South America with OW is the best of any alliance (until TAM joins Star Alliance). But the problem in Africa and Central America is that there is just no airline in this region which is with OW. Each of the three alliances has gaps and holes somewhere. But OW is just the smallest of the alliances so the holes are a bit bigger.

Question 9: I think that has been answered already.