First of all, welcome to FT!

Secondly, yes, this has been discussed to death and then some.

What that rule says, and what it means in reality are sometimes two different things. The reality is that you can only enter Asia twice if one of the entries is a transit, and furthermore that transit is between Europe and SWP (e.g. LHR-SYD) or v.v.

For NA the rule is simpler. Yes, SAO-NRT with a connection in JFK is allowed under the rule as a second entry. Yes, NA must be paid for regardless (you touch it you pay for it). And no, the transit need not be a single flight number; the rule just means your connection time must be under 24 hrs, and you are quite free to connect two flights, e.g. GRU-JFK on AA and JFK-NRT on JL.