The trip from a strict Pakistani boarding school to a bohemian bar in Philadelphia has defined David Headley’s life, according to those who know the middle-age man at the center of a global terrorism investigation. Raised by his father in Pakistan as a devout Muslim, Mr. Headley arrived back here at 17 to live with his American mother, a former socialite who ran a bar called the Khyber Pass. Today, Mr. Headley is an Islamic fundamentalist who once liked to get high. He has a traditional Pakistani wife, who lives with their children in Chicago, but also an American girlfriend...