Why does Vera ask Mr. Nuttel what he knows about her aunt and family?

Saki, the author, wanted to keep the reader in the dark as to Vera's intentions and motives. The girl seems to be making polite conversation with the visitor. It does not become apparent until much later in the story that Vera wants to be sure of Framton's ignorance of local history before she tells him the ghost story she has in mind. If such a tragedy had really occurred, it would have been known and talked about all over the region.

"Do you know many of the people round here?" asked the niece, when she judged that they had had sufficient silent communion.

"Hardly a soul," said Framton. "My sister was staying here, at the rectory, you know, some four years ago, and she gave me letters of introduction to some of the people here."

Once Vera has gotten the information she has been fishing for, she tells him her whole made-up story about the three hunters who got sucked into a bog exactly three years ago. Saki emphasizes that this young girl is "self-possessed," that is, poised, relaxed, sure of herself. She intends to lose her self-possession when the three hunters will appear outside, headed towards the open window. She will fake an expression of goggle-eyed horror to make it appear to the nervous Framton Nuttel that she is actually seeing ghosts. When her aunt, who has supposedly been waiting for them for three years, announces that she sees her men approaching:

Framton shivered slightly and turned towards the niece with a look intended to convey sympathetic comprehension. The child was staring out through the open window with a dazed horror in her eyes.

The girl's imagination and mischievous spirit have turned this stereotypical English country manor into a house of horrors. Framton flees for his life because he is sure the three returning hunters must be ghosts armed with shotguns. It is only after his flight that the reader is let in on Vera's practical joke. The three hunters are just ordinary men returning from a day's snipe-shooting in the marshes. 

"Here we are, my dear," said the bearer of the white mackintosh, coming in through the window, "fairly muddy, but most of it's dry. Who was that who bolted out as we came up?"

"A most extraordinary man, a Mr. Nuttel," said Mrs. Sappleton; "could only talk about his illnesses, and dashed off without a word of goodby or apology when you arrived. One would think he had seen a ghost."