Short answers, pulled from the story.
New Line Cinema was founded by Robert Shaye on the 18th of June, 1967, in New York City. Shaye was 27 years old at the time and initially ran the company from his apartment at 14th Street and Second Avenue.
The nickname refers to the Nightmare on Elm Street franchise, which New Line produced starting in 1984. The first film cost $1.8 million and grossed over $57 million, fueling the studio's expansion, and the first six films in the series grossed $500 million worldwide.
The Lord of the Rings trilogy won 17 Academy Awards out of 30 nominations. The final film, The Lord of the Rings: The Return of the King (2003), won eleven awards including Best Picture, tying the all-time record for wins in a single ceremony.
New Line Cinema ceased operating as a separately managed studio on the 28th of February, 2008, when Time Warner CEO Jeff Bewkes announced its integration into Warner Bros. Pictures. It had previously been acquired by Turner Broadcasting System for $500 million in January 1994.
Teenage Mutant Ninja Turtles (1990) grossed $135 million in the United States and Canada, making it the highest-grossing independent film of all time at that point. It held that record until The Blair Witch Project surpassed it in 1999.
The Golden Compass (2007) was largely blamed for the decision. New Line spent $180 million on its development but the film grossed only $70 million in the United States market. The studio was merged into Warner Bros. Pictures in 2008.