Short answers, pulled from the story.
Langley Research Center was established in 1917 by the National Advisory Committee for Aeronautics (NACA). It was created following a 1917 Aviation Week warning that U.S. military aviation lagged behind European capabilities, prompting President Woodrow Wilson to order the creation of the nation's first aeronautics laboratory.
NASA Langley Research Center is located in Hampton, Virginia, near the Chesapeake Bay front of Langley Air Force Base. It is the oldest of NASA's field centers.
The West Area Computers were African American female mathematicians who worked as human computers at Langley Research Center from 1943 through 1958. They were segregated from white mathematicians under Virginia's Jim Crow laws and worked in Langley's West Area.
Houston, Texas was selected over Langley Research Center for NASA's Manned Spacecraft Center, despite Langley's prominence with NASA, the large aerospace industry in the Hampton Roads region, and its proximity to Washington, D.C. The decision came as a surprise to many senior Langley officials and caused lingering controversy over job losses to Houston.
The hypersonic X-43 achieved a world speed record of Mach 9.6. LaRC supported its design and testing.
The Lunar Landing Research Facility opened at Langley in 1965. It used a gantry to suspend a mock Apollo Lunar Module above a simulated lunar landscape, allowing astronauts to practice Moon landings under simulated lunar gravity conditions.