what are the possible reasons which pushed the US government to keep secret this amazing discovery
The US Government at this time was INCREDIBLY paranoid, and totally committed to trying to protect the status quo by whatever means necessary. Discovery of proof of intelligent alien life would, if nothing else, be incredibly destabilizing and for these people, keeping it absolutely secret would be a no-brainer. Allowing the discovery to go public would cause massive social and political upheaval, and would likely spur the Soviet Union to double down on their own space program to ensure they weren't left out.
Bonus question : - For what reasons did US government stop the Apollo program and thus the exploration of the vestiges as soon as 1972 ?
Easy: They didn't. Instead they took the entire lunar program and put the entire thing under the tightest secrecy possible.
Remember: The US Government's primary objective at this point is to keep the Soviets as far away from the moon as possible. The best way to do this is to make the moon look BORING.
They finish out the Apollo program by using the subsequent missions to gather as much information about the artifacts as possible with the technology possible. Then they shut it down, at least publicly. The USA is Done with the Moon, and the Soviets chalk it up as a Loss and move on to new things.
In the meantime, a massive secret program launches to analyze all the images and artifacts returned from the moon. Many of the spectacularly sophisticated and expensive Keyhole reconnaissance satellites are actually put into Lunar orbits rather than taking pictures of Soviet missile sites. The United States put up a desperate front to convince the USSR that the entire attention of the United States scientific and military establishment is still focused on the prospect of confrontation with the Soviet Union, while instead those resources are entirely focused on the moon.
In 1973 NASA launches Skylab. Ostensibly a primitive attempt to explore the challenges and possibilities of orbital space stations, Skylab is actually intended to be an orbital launchpad and refueling station for a new series of lunar expeditions. The technical challenges associated with trying to SECRETLY get the second generation lunar modules into orbit and launched into lunar trajectories prove to be insurmountable however, and in 1978 the program is shut down.
In 1983 the deployment of the Space Shuttle finally gives NASA the tools they need to quietly return to the moon. Contrary to popular opinion, the stealth programs headlined by Lockheed's Skunk Works have had the primary objective NOT of developing stealth aircraft, but rather the creation of stealth SPACECRAFT that can be carried into orbit by the space shuttle to come and go from the moon in secret.
Completely unbeknownst to all but the inner circle, every third shuttle launch actually carries a stealth second-generation Apollo module outfitted with Radar Absorbent Materials and ECM. Once in orbit the new "Hermes" modules quietly make their two-week journeys to the moon and back with mixed crews of astronauts and specially trained scientists.
The moon program is shut down along with the shuttle after the Challenger disaster results in the loss of not only the publicly acknowledged shuttle crew, but also a fully crewed lunar probe with six more astronauts and scientists, including the project lead.
Missions continue, although at a reduced frequency, until the loss of the Columbia in 2003. The grounding of the shuttle fleet immediately afterwards required an emergency re-entry procedure to be executed a week later by the returning crew of the final second-generation lunar mission, as the shuttle mission that had been scheduled to ferry them back down to earth had been cancelled.
This marks the end, at least for now, of manned exploration of the moon, although over the two and a half decades a massive trove of detailed examinations and artifacts have been collected that will keep an army of exo-archeologists busy for a generation.
EDIT: In a moment of extreme irony, NASA themselves conceive and propagate the idea that the moon landing was faked, adding another layer to the smokescreen and helping support the idea that the moon is Boring.