The gravity inside the Jamestown lunar base appears to be normal in that the characters are able to work around and handle objects in the same way they would on Earth, even though the force of gravity on the surface of the Moon lower than it is on the surface of the Earth. However, lunar gravity kicks in when the characters are outside the lunar base.
The 1967 Treaty on the Peaceful Uses of Outer Space bans governments from putting weapons in space. The US and USSR were parties to this Treaty and the treaty remains in force to this day.