Short answers, pulled from the story.
George Lucas watched Akira Kurosawa's 1958 film The Hidden Fortress and saw a peasant character named Matashichi. That small, round figure became the visual seed for R2-D2. Artist Ralph McQuarrie drew early concept art that blended this influence with robots from Douglas Trumbull's 1972 film Silent Running.
Sound editor Walter Murch asked for Reel 2, Dialog Track 2 while working on an earlier project. He spoke the phrase aloud as R-2-D-2. Lucas had dozed off in the room but woke when he heard the request. He called it a great name before returning to his script.
English actor Kenny Baker performed inside the original R2-D2 suit for all three Star Wars films. Deep Roy served as Baker's double in Episodes V and VI, providing stunts when Baker was unavailable. Jimmy Vee co-performed the character in some scenes before taking over fully starting with The Last Jedi.
R2-D2 carries information discs containing Death Star plans aboard the Tantive IV when Princess Leia hides them inside him. He helps rescue Princess Leia and delivers Death Star plans to the Rebel Alliance. During the battle, he is severely damaged but repaired before the final ceremony.
The Walt Disney Company acquired Lucasfilm in 2012 and rebranded most licensed novels and comics as Star Wars Legends in April 2014. These stories were declared non-canon to the franchise following that decision. The Expanded Universe novel The Swarm War contains an electronic glitch that unearths images of Anakin relating his fear of losing Padmé.