Short answers, pulled from the story.
Buzz Aldrin's first words after setting foot on the Moon were "Beautiful view." When Neil Armstrong asked if it was something, Aldrin replied, "Magnificent desolation." He stepped onto the lunar surface at 03:15:16 UTC on the 21st of July 1969, nineteen minutes after Armstrong.
The Aldrin cycler is a spacecraft trajectory proposed by Buzz Aldrin in 1985 that makes repeated travel to Mars more efficient by using less propellant. It provides a five-and-a-half month journey from Earth to Mars, with a return trip of the same duration on a twin cycler orbit. Aldrin continues to research this concept with engineers from Purdue University.
Buzz Aldrin, a Presbyterian elder, took communion on the lunar surface after the Apollo 11 landing, making him the first person to hold a religious ceremony on the Moon. He kept the ceremony private because of a lawsuit that had followed the reading of Genesis on Apollo 8. In 1970 he noted that the communion wine and wafer were the first liquid poured and first food eaten on the Moon.
Early versions of the EVA checklist had the Lunar Module pilot stepping out first, but multiple factors led to Armstrong going first instead, including the physical layout of the compact lunar lander, which made it easier for Armstrong to exit. Aldrin lobbied within NASA for the original procedure but had little support among senior astronauts. Michael Collins later commented that he thought Aldrin resented not being first more than he appreciated being second.
After leaving NASA in 1971, Aldrin suffered from clinical depression and alcoholism that he recounted in his autobiographies Return to Earth (1973) and Magnificent Desolation (2009). He was hospitalized for depression at Wilford Hall Medical Center, worked unsuccessfully selling used cars, and was eventually arrested for disorderly conduct. He quit drinking in October 1978.
Buzz Aldrin flew 66 combat missions in F-86 Sabres during the Korean War and shot down two MiG-15 aircraft. For his service he was awarded two Distinguished Flying Crosses and three Air Medals. His tour ended in December 1953.