Short answers, pulled from the story.
The character Claire Temple was created as a composite of two Marvel Comics characters, Claire Temple and Night Nurse, also known as Linda Carter. Showrunner Steven S. DeKnight noted that the character was originally going to be the actual Night Nurse from the comics, but plans for the feature side to use her necessitated the change to using the more obscure comics character Claire Temple as her name.
Rosario Dawson joined the cast of Daredevil in June 2014. Her role was revealed to be that of Temple in October of that year.
Claire Temple arrived in Harlem where her mother runs a diner in Luke Cage. She has since reprised the role in Jessica Jones in 2015, Luke Cage from 2016 to 2018, Iron Fist from 2017 to 2018, and The Defenders in 2017.
Claire Temple quits her job at the hospital when it tries to cover up the death of her coworker following an attack by The Hand. She leaves Hell's Kitchen and arrives in Harlem where her mother runs a diner.
Dawson was nominated for Outstanding Supporting Actress, Drama Series for Luke Cage at the 2017 Black Reel TV Awards and for Outstanding Supporting Actress, TV Movie or Limited Series for The Defenders at the 2018 Black Reel Awards.