Dumb question: What gives NASA the authority to build anything on the moon?
This is why chemical weapons treaties are signed and obeyed, while land mind treaties are not: the military of powerful countries doesn't seem chemical weapons as something they want, while landmines are useful in some situations. (If your country has signed a land mind treaty it is probably because they can count on an allied country that hasn't to place land mines. If your country hasn't signed a chemical weapons treaty it is because your military isn't very good by modern standards and so you can accept the downsides)
Basically anything goes as long as it's not for military purposes.
Article IV says: "The use of any equipment or facility necessary for peaceful exploration of the moon and other celestial bodies shall also not be prohibited."
But I wouldn't be surprised if this is new territory for law and sovereignty on the moon, and will be a bit controversial.
Building anything else is perfectly fine, as long as you don't claim ownership over a portion of a celestial object.
Yet, people and country who get there first usually get to name it, but then that's a touch of concern in todays times of #colonization yet it has succeeded and failed when you look at USA, Spain, UK, France....
Meanwhile, would any viable competitors in terms of China and Russia honor and think about this as if "NASA" has authority vs "they were first too?"
So, #America!
In the grand scheme of things, USA has been much much fair in terms of diplomacy across the world, from shipping channels and helping peace (through war, unfortunately, sometimes) vs China or Russia.
So it's a good question, really good.