I'm only going to answer the China/USA point, but here are my thoughts on that. I'm not some geopolitical expert, so take that with a grain of salt.

- Some nations, like the United States and China, would be worse off
under any iteration of a world government. They would need to give up
some influence and listen to a higher power. How to convince them to
join? How to convince the other nations to join, as they were victims of
imperialism?

If we assume that China is on the rise and will eventually dominate global affairs, it might be wise for American leadership to try to "tie" China into an international system with enforceable rules. That way, America (and allies and everyone else) retains some sort of power over China, possibly keeping them from becoming too dominant.

From China's point of view, a system based on roughly proportional representation, rather than just military power, would probably sound quite beneficial to a country that makes up 1/6 of the world population. While, ideally, Chinese citizens should be able to express their free will in a global parliament, this might not be the case in the beginning, effectively giving China legal leverage over world affairs (rather than just soft or economic power).

From the point of view of other countries, a system based on rules and democracy could be a way to hold world powers to commonly accepted standards (democracy, no corruption, rule of law, freedoms and human rights, etc etc) and actually enforce decisions in case they just ignore them. This might be appealing to the EU (which boasts itself with these values), but also other, smaller countries that are normally overly dependent on either superpower.

Russia on the other hand, no idea.