I don't know the specifics of Brazil's system, but at least in the US gerrymandering has nothing to do with the Presidency or Senate, only the House. It's also not without risk. Gerrymandering is bad, but it doesn't change the totals of votes; it attempts to reapportion "excess" votes yielding a large win margin in one area to give winning, but necessarily smaller, margins in more areas. Amongst other challenges though that smaller margin means if there is a wave then a gerrymander can turn into a "dummymander" where previously safe districts get flipped.
>funny business
This is actually pretty dang hard in anything but a total sham, and even then is at least obvious it happened. Some timy fiddling at the margins may be possible to sneak through, and yeah some elections that might make the difference. But that can't counter any serious victory. The more common technique seems to be trying to suppress the vote. But as well as also not being trivial it also too risks backfiring by motivating people much harder. There is a lot of human psychology around "loss", people often absolutely hate things being taken from them even if they were complacent about having them.
Must win by 50% plus 1 of all valid votes on Round 1. If not, 1st and 2nd most voted go for Round 2 a few weeks later. Then, 50%+1 again of all valid votes.
Everything else you mentioned also matters. I can't tell you the amount of times that the state of Georgia, suddenly out of the blue, invalidated a lot of registered voters. And if people don't check, like my friend in a minority town outside of Atlanta, they won't realize until election day. Red states are more likely to play this trick. Your conclusion is something I disagree with, though. Voters have lost so much over the last decade, and they don't fight back until it really starts to affect them personally. I think the surge that we might see this election is only due to economics. If the economics were good, it's not out of the question that Trump would be doing fairly decent this election cycle. This is why Iran is playing things very well to try to enact maximum economic pain in the days before the election. But it's all about economics, and that shows you that people truly don't really care.
Well it does change which voters decide the results. A lot of electoral systems seek to constantly redress imbalance by having impartial bodies redraw district lines as populations shift. It is a shame the US does not. Gerrymandering is fundamentally undemocratic.