Short answers, pulled from the story.
Harry, Albert, Sam, and Jack Warner established Warner Bros. Pictures on the 4th of April 1923. This new entity replaced their earlier venture known as the Warner Features Company which they had operated since 1910.
Kinney National Company purchased Warner Bros.-Seven Arts in 1969 during an aggressive acquisition period. The buying spree included National Periodical Publications which later became DC Comics and Television Communications Corporation which was a predecessor to Time Warner Cable.
Warner Bros. Cartoons began operations in 1929 and continued until 1963 while producing animated shorts that defined American entertainment. Warner Bros. Television Studios started work in 1955 and remains active today alongside music publishing activities through Warner Bros. Music.
AT&T acquired Time Warner on the 15th of June 2018 and renamed the combined entity WarnerMedia. Discovery Inc. purchased WarnerMedia from AT&T to form Warner Bros. Discovery on the 8th of April 2022.
Only Warner Records continues to carry the Warner name among these spun-off entities after Time Warner spun off Warner Music Group during the mid-2000s. Other former subsidiaries like Warner Books were sold to Hachette Livre and Time Warner Cable later became part of Charter Communications.