Short answers, pulled from the story.
The Defense Advanced Research Projects Agency was created on the 7th of February 1958 following the launch of Sputnik 1 by the Soviet Union on the 4th of October 1957. President Dwight D. Eisenhower signed the order to establish the agency to prevent future technological surprises and ensure national security.
Roy Johnson served as the first director of DARPA after leaving a $160,000 job at General Electric to accept an $18,000 position at the agency. Herbert York, Johnson's scientific assistant, came from Lawrence Livermore National Laboratory and brought expertise in the nuclear age to the new organization.
DARPA funded the creation of ARPANET which went online in 1969 and served as the first wide-area packet switching network. The agency also supported the development of time-sharing, the Multics project, and hypertext systems including Douglas Engelbart's NLS computer system which introduced the mouse.
The Information Awareness Office established in 2001 developed the Total Information Awareness program to gather personal emails, social network data, and medical records without a search warrant. The agency also launched the LifeLog Project in 2004 to collect all data about an individual before it was shut down due to public backlash.
DARPA funded the development of BigDog a four-legged robot designed to carry heavy loads over rough terrain and the Adaptive Suspension Vehicle nicknamed the Walker. The agency also supported the Gremlins program involving air-launched UAVs and the Manta Ray program for autonomous underwater vehicles.
DARPA is developing the Hypersonic Air-breathing Weapon Concept HAWC and the Tactical Boost Glide program to create air-launched hypersonic missiles. The agency also funds the Glide Breaker program to intercept maneuvering hypersonic vehicles and the High Energy Liquid Laser Area Defense System to intercept incoming missiles.