The five most popular story-specific questions about The Feud, season 1, episode 4, excluding overall plot and ending, are:

1. What life-altering news does Babe Paley receive in this episode?
2. How does Babe Paley's health condition affect her actions and relationships?
3. What is the significance of Truman Capote's plan to host a sequel to the Black and White Ball?
4. How do Babe and Truman Capote reflect on their broken friendship in this episode?
5. What themes of grace and forgiveness are explored through the characters' interactions?

These questions focus on key story elements such as Babe's cancer diagnosis and treatment, the social dynamics around Truman's ball, and the emotional reconciliation attempts between Babe and Truman, as depicted in episode 4 titled "It's Impossible".