Re: the Brazil visa, according to this article https://thepointsguy.com/2017/10/brazil-e-visas/, effective January 28, it will be possible to apply for an e-visa, eliminating the need to visit a Brazilian consulate/embassy and tying up your passport for several days.

As far as miles, I once used AA miles for the outbound segment of a trip to BKK on Cathay Pacific and then some leftover UA miles to get to NRT (nonrevved back to the US from NRT on AA). I called to see what was available and booked. Miles seem harder to use nowadays and the amount of miles needed has gone up so don't have recent experience. We do get a 20% discount on AA miles if booked on AA metal. Depending where in Asia you plan to go, I would try to go direct as AA has more flights to Asia than they did a few years ago (although I'm very upset they got rid of the JFK-NRT nonstop - used to always be able to get F!). First Japan trip nonrevved both ways with backup zeds. It's much easier to book zeds now that everything is electronic. Once you get to Asia, there are LCCs that seem reasonably priced. Depending on where you are flying from, I would try AA with backups on UA, DL, JL, CX and a handful of others we have agreements with. If your intent is to include South America in your travels, QF and LA fly to SYD and AKL from SCL and NZ from EZE to AKL. That said, those are long flights to be stuck in the back. Hope this helps!