Short answers, pulled from the story.
NASA approved the two-man program rechristened Project Gemini on the 7th of December 1961. The program was publicly announced on the 3rd of January 1962 after McDonnell Aircraft was contracted to build it on the 22nd of December 1961.
Project Gemini aimed to demonstrate human endurance for extended periods up to two weeks, effect rendezvous and docking with another vehicle, and demonstrate Extra-Vehicular Activity or space-walks outside the spacecraft. It also intended to perfect techniques of atmospheric reentry and touchdown at a pre-selected location on land.
Jim Chamberlin was the main proponent of using aircraft-style ejection seats for the emergency launch escape system in Project Gemini. Maxime Faget designed the Mercury LES but feared the ejection seats might seriously injure astronauts and noted they would only be usable for about 40 seconds after liftoff.
Elliot See and Charles Bassett were killed when their trainer jet crashed into a McDonnell building holding their capsule in St. Louis in January 1967. These deaths forced immediate reshuffling of all remaining assignments including moving Stafford and Cernan up to become prime crew of Gemini 9A.
From 1962 to 1967, Project Gemini cost $1.3 billion in 1967 dollars totaling approximately $797 million for spacecraft plus $409 million for launch vehicles. The program left Apollo free to pursue its prime mission without developing techniques themselves.