Brazillian here. Under brazillian law, since around 1998 the armed forces can take down what they consider to be hostile aircraft. And since 2019, they no longer need authorization from the president nor an air force high-ranking official.
There are some criteria to be met in order for an aircraft to be considered hostile. The TL;DR is that you are hostile aircraft if you can fly (seriously, the law used to list balloons and paragliders as possible targets for takedown) and any of the following is true:
- you don't identify (or misidentify) yourself;
- you knowingly put people or property in danger;
- you pack weaponry, without written authorization from the armed forces.
If your hero has the courtesy to fly around with a transponder and happens to be even slightly popular among brazillians, the government will grant him passage and authorization to carry (and possibly use) weapons while flying. They will even spare him the red tape.
Otherwise... I don't think Brazil has much in the way of taking him down (we might have bought a dozen hypersonic missiles from the US and EU at some point), but dude had better not spend a night on brazillian soil. If the military doesn't get him, the organized crime will get him and deliver him to the military. And the usual treatment given to people who think they are above the forces is anal rape with a broomstick. Sadly and unfortunately, as well as much to our national shame, this is not a joke by any means. I mean it. This is so entrenched in our culture that we don't even flinch anymore when this is shown in a movie.
As to the minimum altitude the hero would have to be flying incognito while not pissing the brazillian air force off, that would be higher than 24,500 ft (~7,468 m) above sea level AND not passing through any airway.
Regardless of treating the hero as a friend or a foe, his case is so special that the brazillian government probably would not require him to have a pilot's license.
As far as other countries in South America go, the vibes I get is that the lower than GDP and HDI, then obviously the less capacity they would have to catch or counter the hero, but also the less friendly they would be. Argentina, Chile and Uruguay would probably follow Brazil in how to deal with him, might even team up. Venezuela on the other hand won't be able to do a thing and will absolutely hate the hell out of the guy, as in a scheduled 2-minutes-hate show on TV on a monthly basis. French Guiana will at the very least demand that he be careful when passing by since they often send rockets to space on behalf of the ESA, the european equivalent to NASA. Keep in mind that French Guiana is part of France and thus messing up with it is messing up with the EU and NATO.