On the night before her shocking death, Dorothy Kilgallen, a star panelist on the hit TV game show “What’s My Line?” correctly guessed the occupation of a mystery guest: a woman who sold dynamite. The glamorous, razor-sharp Kilgallen delighted viewers, but behind the scenes, the dogged and courageous reporter was hot on the trail of the biggest story of her life: the assassination of President John F. Kennedy. The morning after that show, on Nov. 8, 1965, the 52-year-old newspaper columnist hailed by The Post as “the most powerful female voice in America” was dead in her Manhattan town house....