I suspect that you might possibly remember details from two or more different novels which might not be in the same series.
I remember another old science fiction novel with teenage astronauts on the Moon, by Hal Clement, which should probably be The Ranger boys in Space, 1957.
I remember that in that novel it was discovered that adults were incapable of tolerating the feeling of weightlessness in space but kids could. The rockets used steam - they heated up water to steam to be the propellant. I also remember a scene with spies attacking a house on Earth early in the plot, about the time when the boy protagonists are recruited as astronauts. And a scene on the moon where one of the boys falls into a pit. Since gravity on the Moon is only one sixth that on the Earth the boy calculates that he should be able to jump out of the pit. But he can't. He finally realizes that his calculation was wrong because he divided by six two times, once for the height and once for his weight, and he should have divided only one of those factors by six.
Here is a link to a site with reviews and synopsis:
There is also Robert A. Heinlein's first juvenile novel Rocket Ship Galileo, 1947.
A nuclear physicist has invented a new form of atomic energy soon after World War Two. His attempts to promote it get him fired from his job. He recruits high school boys to help him built a rocket ship using his atomic engines. He makes an expedition to the Moon with the boys and they discover that Nazis have secretly built a moon base there and plan to conquer the Earth.
A plot summary is here:
In The Voyage of the Luna 1, David cragie, 1947, two primary school children stowaway in the first unmanned rocket to land on the Moon.
Many plot details are mentioned in my answer here:
Children stow away to the moon
I also remember reading a juvenile novel where an Australian boy goes on the first voyage to the Moon.
I asked a question about it here:
YA Australian based flight to moon from area near meteor craters3
The best answer I got was Moon Ahead, by Leslie greener, 1951.
There are 21 novels in the Chris Geoffrey of U.N.E.X.A. series by Hugh Walters. I have read one, in which a teenager goes on a mission to the Moon with adult astronauts. I remember that strange mists moved over the lunar surface.
From the synopsis, I believe it is Moon Base One, 1960. The synopsis says:
Thousands of young people are terminally ill as a result of the radiation produced by the lunar structures destroyed in The Domes of Pico. In an attempt to determine whether the fall-out from the domes can have a curative effect on the disease a joint East-West mission is planned under the auspices of the newly formed United Nations EXploration Agency (UNEXA).
The mission is commanded by Chris Godfrey, accompanied by American, Morrison 'Morrey' Kant and Russian Serge Smyslov. The 'patient' will be Tony Hale, from Aston near Birmingham (who goes on to feature in the rest of the series). The mission starts well, but is soon in trouble when a supply rocket crashes...
In the first novel in the series, Blast off at Woomera, 1957, Chris Geoffrey is a small for his age teenager, the only persons both qualified and small enough for the mission. The Synopsis says:
Strange objects have been sighted on the Moon near Mons Pico. Suspecting a communist plot, the British Government hurriedly plans a mission to photograph the domes from above closer range. The rocket is not large enough to send a man - enter Chris Godfrey, a 17-year-old science whiz with an interest in rocketry and crucially less than 5 feet tall!
The launch site is Woomera Rocket Research Station in South Australia, but there may be a Soviet traitor amongst the ground crew...
The book pre-dates the first actual usage of satellite imagery by two years, and manned spaceflight by four years.
I remember seeing the cover of a paperback novel in which US and USSR spacemen fought on the Moon with sub machine guns. That novel might possibly be the one with the conflict you remember. Unfortunately I don't remember the title of that novel, and there could have been a bunch of other novels with Cold War conflicts on the Moon.
SteveV's suggestion The Master of the Moon, by Patrick Moore, 1952, might also be a book you partially remember.
I have copied SteveV's link to a synopsis:
There was a company which published a bunch of science fiction novels by various authors.
Winston Science Fiction was a series of 37 American juvenile science fiction books published by the John C. Winston Company of Philadelphia from 1952 to 1960 and by its successor Holt, Rinehart & Winston in 1960 and 1961. It included 35 novels by various writers, including many who became famous in the SF field, such as Poul Anderson, Arthur C. Clarke, Ben Bova, and Lester del Rey. There was also one anthology, The Year After Tomorrow, edited by del Rey and others. There was one non-fiction book Rockets through Space: The Story of Man's Preparations to Explore the Universe by del Rey which details the factual science and technology of rocket flight. Many of the dust jackets became science fiction classics; the artists included Hugo Award winners Ed Emshwiller and Virgil Finlay along with Hugo nominees such as Mel Hunter and Alex Schomburg.
If you read several different Winston Science Fiction books by different authors, you might think that they were part of a fictional series instead of separate stories.
Here is a link to a photo of the endpapers in the Winston books:
I remember the titles and/or plot details of seven of those books, so I can eliminate those seven - Islands in the Sky, Planet of Light, Vandals of the Void, Trouble on Titan, The Secret of the Martian Moons, The Secret of the Ninth Planet, and Stadium Beyond the Stars, leaving the remaining thirty as possibly being part of your memories.