Short answers, pulled from the story.
NASA leadership selected Neil Armstrong as the first person on the Moon because they wanted a calm and quiet figure to embody the role, unlike Buzz Aldrin who was considered too volatile. The decision was a calculated political strategy that prioritized Armstrong's unflappable coolness over Aldrin's aggressive lobbying for the historic moment.
The Soviet Union launched Luna 15 on the 13th of July 1969, just three days before Apollo 11 launched. This probe reached lunar orbit before Apollo 11 but crashed in Mare Crisium about two hours before Armstrong and Aldrin lifted off from the Moon.
The 1201 and 1202 program alarms were caused by a hardware design bug in the rendezvous radar system that left the radar in the wrong position. This error caused the computer to process data from both the landing and rendezvous radars simultaneously, creating an involuntary counter that stole processing cycles from the landing software.
The Lunar Module Eagle touched down with less than 30 seconds of fuel remaining, though post-mission analysis suggests the actual figure was closer to 50 seconds. The premature low fuel warning was the result of propellant sloshing more than expected, which uncovered a fuel sensor.
Neil Armstrong stepped off the ladder of the Eagle at 02:56:15 UTC on the 21st of July 1969, six and a half hours after landing. This event marked the first time a human walked on the Moon, with the broadcast received by at least 600 million people on Earth.
The Interagency Committee on Back Contamination lifted the quarantine on the astronauts and Columbia on the 10th of August 1969 in Atlanta. The crew had been in Earth-based quarantine for 21 days following their return to Earth on the 24th of July 1969.