Short answers, pulled from the story.
The idea for such a list started on the 1st of February 1998, with a debate at a symposium in Hanoi, Vietnam. The panel participants were former CBS Evening News anchor Dan Rather, historian Doris Kearns Goodwin, former New York governor Mario Cuomo, then Stanford Provost Condoleezza Rice, publisher Irving Kristol, and Time managing editor Walter Isaacson.
Time recognized Albert Einstein as the Person of the Century in an issue published on the 31st of December 1999. Editors believed the 20th century will be remembered foremost for its science and technology and argued Einstein served as a symbol of all scientists who built upon his work.
Essayist Nancy Gibbs addressed the topic with the article The Necessary Evil? published in the same the 31st of December 1999 issue. She argued that both men went about their carnage with efficiency perfected by modern industry while critics questioned if evil could ever be more powerful than genius or creativity.
Time magazine representative Bruce Handy defended the choice by noting Elvis did not write his own material unlike The Beatles or Bob Dylan. He claimed The Beatles pushed the envelope further while Elvis most original recordings came early.
The magazine also included fictional character Bart Simpson from The Simpsons television series among the 100 most influential people. Handy explained cartoons were one of our great contributions along with jazz and film.