I guess this legal battle is futile. America has already place many flags on the moon. So the moon belongs to america.

Not so quick. When the American Astronaught landed on the moon, he found Indians were already there.

I guess it goes back to the debate of who arrived in america first, Leif Erickson or Christopher Colombus or the Amerindians

If we are going to conquor space it will not be as Chinese or Russians or americans or whites or blacks, but as humans. It is not a place were any one group can nationalize and dominate. The moon will not be accessible to whole scale colonization by us in another 100 years. Mars not for another some 500 years and by the time we get to the moons of Jupiter and Saturn we will be barely ready for beyond that.

One hardly knows the political organization that will exist in 50 years. China was ( and for the most part) a destitute nation unable to take care of itself in 1980. It is the US that bootstrapped it into existence. The Soviet Union extended across a third of the globe with satellites from east to west. Despite Putin it remains a  satellite western nation. Now it is fraction its size. China may exist as two states, the US as many or all nations  as a global consortium as an earth corporation. We do not know.

It takes just one crisis. A global pandemic or an asteroid strike of a mid Ocean earth quake or even a human generated disaster etc to put everyone into interdependent mode. It is inevitable that is where we function best and that is the inevitable state for best management of large problems. The only thing we know is that Space cannot be nationalized and conquered by any one group except if it is a human group

I don't believe they are going to allow Africans or Hindus on the Moon, and these will not be able to make it to the Moon even if they are the only survivors of a global cataclysm 

They have no choice. By the time we can  get there the color line will be quite "browned down".

"China's technological advances" is an oxymoron. The US advances the technology. China just steals it and copies it.