There's some legal stuff re: weaponisation of space in the Outer Space Treaty, but it doesn't apply to bases on the moon. The USA could put one up there, Elon Musk could, China could, Russia could, the ESA, India and so on can all place a base there if they want to.

Exactly, but imagine a future, lets say 100 years from now, people have started to occupy Mars, the moon has become a stopover, and has been occupied completely.

People don't get along on earth, let alone in space, with no laws, no rules, and no legal property.

I'm trying to imagine this scenario, and try to find solutions for a non existing problem, but I don't doubt that there will be conflict over this, and since there's nothing to claim laws should eventually be made, and pacts between nations in order to make this work.

It might seem far fetched, but I really don't think it is.