The role of the women at NASA is the subject of "Hidden Figures," a 2016 movie based on a book by the same name recounting the true story of the African-American mathematician Katherine Johnson and her two colleagues, Dorothy Vaughan and Mary Jackson, who, while working in the segregated West Area Computers division of Langley Research Center, helped NASA catch up in the Space Race.
The speech that President Nixon gives is taken from a speech that was prepared in case Apollo 11 was failure.
The three astronauts shown in the pictures on the wall were Command Pilot Virgil I. "Gus" Grissom, Senior Pilot Edward H. White II, and Pilot Roger B. Chaffee, all of who died in a cabin fire during a launch rehearsal test of Apollo 1.
Lockman Aerospace is an amalgamation of real-life aerospace companies Lockheed and Grumman. Lockheed and Grumman were both part of the space race, with Lockheed making escape and control motors for the Apollo aircraft, and Grumman constructing the lunar modules.
Along with Kathrine Johnson; Mary Jackson and Dorothy Vaughn were the other two real-life women that were portrayed in the movie "Hidden Figures" that Rufus alludes to. When he comes back he could actually have met Johnson in "real" life. As of this writing, Kathrine Johnson is the only living person of the trio at age 98.