Simply containing each number sequence is a significantly weaker property than having them all occur at the right frequency. Still, while nobody has proven it, it's generally expected to be true.

Figuring it out on your own is science, but I have a feeling OP didn't actually personally search the world for one-horned horses or pointy eared-people with long lifespans. I bet they didn't even work out how biology changes with scale and how evolution works to show that there can't be tiny winged people.

And how do you get people to collaborate? People have tried making governments based on the idea of everyone working together for the common good. It never ends well.

Ownership in general isn't some fundamental inalienable right. It's just that if you let people own things, you give them more incentive to make things. I think intellectual property rights are far too extensive, but if we didn't have them at all, how would we pay for R&D? How would we pay for big budget games and movies? Maybe you're happy contributing to openly licensed projects, but a lot of people have to pay for rent and raise a family, and can't take the time to contribute to things like that even if they want to unless they have the money to support themselves.

Sure it does. All they have to do is fire the CEO and they'll have so much more money.

Is it ethical to give tools to a country you don't trust to use them responsibly?

If someone is executed for murder, then you definitely shouldn't hire them. But if they served their punishment, letting them out of jail and then not letting them earn the money the need to survive is a recipe for disaster.

I feel like having no way to legally get food or shelter would make it more likely they'd commit crime again, not less.

Isn't that how they got on and off the moon?

If you the download size is in the gigabytes and need a good graphics card to run it, you're doing it locally. Otherwise, it's remote.

Whether or not the US is oppressive is a matter of debate I don't want to get into, but they definitely spy on their own people. And I imagine they're a lot more likely to act on information about someone living in the US than China is.

There is some optimal amount of thermostat vs fan speed. Whether you're better with a lower thermostat and higher fan speed or vice versa depends on which side of this optimum you're on. We as random internet strangers have no way to find this.