The five most popular story-specific questions about The Librarians: The Next Chapter, Season 1, Episode 9 "And the Feast of the Vampire" are:

1. How does Connor avoid turning into a vampire during the small-town festival?
2. What vampire-slaying skills does Vikram teach Charlie in this episode?
3. Who is Peter, the vampire Connor encounters, and what makes him different from typical villains?
4. How does this episode develop Connor's character and his curiosity about magical creatures?
5. What are the implications of the vampire storyline for the larger magical chaos affecting the Library and the team?

These questions focus on the episode's vampire-themed plot, character interactions, and the unfolding supernatural challenges faced by the Librarians.