As for the second point, yes and those examples are also cases of restricting their own citizens. Hence the discussion is still about rights of the citizenry versus their own government restricting them, not "rights" of companies as you put it.
The world is free to not use YouTube and always has been. And by the way I don't agree with many of the major websites' censorship decisions in the last couple years either. They depict only what a loud subset of America thinks is right.
Companies generally make money by serving people. I suppose there are business models where this isn't so (e.g. they exist to sue people or something, but exploiting govt's ability to take money by force instead), but in YouTube's case, they entice people the consensual way.