1. Depending on the country on average the rich live a decade or two longer than the poor, any technology that would allow humans to live hundreds of years would be far too expensive for the average person. It could also be monetized in a way that would enable a new form of slavery where your life would be extended for years so you can work for pennies on the dollar.
2. We aren't doing that now never did it before but we are going to do that when there's less people because of reason...
3. You would run into the same problem as number 1 where the rich would dominate space exploration as they do now and these explorations would be their own thiefdom away from earth and all of its laws.
There would be tons of genocide, death and forcing people to do shit just like now, your problem isn't population number it's that you ignore human nature. In your alternate reality humans seem to have stopped being selfish, greedy assholes.
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Except for the fact that we have more than enough resources to feed, house and take care of everyone in luxury. We had more than enough in the past and we do now, having less people isn't going to magically turn humans into beings that will sacrifice and compromise for the good of the species and the planet. We could have stopped climate change decades ago even now we could make a huge dent but we don't because that's not who we are. When it's too late then people will demand action, climate deniers are still getting elected we obviously don't give a shit.