Short answers, pulled from the story.
The National Advisory Committee for Aeronautics first awarded this medal before the space agency existed. The organization changed its name to NASA in 1958 and inherited the award shortly after.
Alan Shepard received his award on the 8th of May 1961 following his historic suborbital flight. John Glenn earned the medal in 1962 after becoming the first American to orbit Earth.
Presidents may award an even higher honor called the Congressional Space Medal of Honor based on recommendations from NASA. This distinction sits above the Distinguished Service Medal in the federal hierarchy of space decorations.
Wally Schirra holds the record for three separate awards spanning decades of service. Kalpana Chawla received the honor in 2004 before her tragic loss aboard the Space Shuttle Columbia.
Officials replaced that initial design with a Type II medal later that same year. The current Type II version displays the official NASA seal upon its face.