Why do you think the young lady asked Framton the initial set of questions?

Vera asks Nuttel all the questions because she wishes to set him up for a scare. She knows he is down for a "nerve" cure and so thinks it would be fun to truly frighten the already nervous man. He comes across as a bore, so Vera probably also wants to get rid of him as a guest.
When Vera learns he knows nothing of her aunt or her family or any of the people in the area, she is then free to tell him almost any story she wants and be believed. Because Mr. Nuttel doesn't realize that her aunt's husband and two brothers are alive, Vera makes up a story that they disappeared a year ago and are presumed dead, but she says that her aunt leaves the window (we would call it a French door) open in the hopes they will return. When Mr. Nuttel sees the very much alive threesome coming home, he thinks he is seeing ghosts and flees.

At the beginning of the story, Framton Nuttel arrives at Mrs. Sappleton's home with a letter of introduction and is greeted by her mischievous niece, Vera. Vera initially asks Mr. Nuttel if he knows anyone from around the area and if he is familiar with her aunt, Mrs. Sappleton. Framton responds by telling Vera that he knows absolutely nobody from the area and only knows Mrs. Sappleton's name and address. Vera then begins to tell Mr. Nuttel a made-up story about why her aunt leaves the French window open. The reason Vera initially questions Frampton Nuttel is to understand his background better and discern if he is gullible enough to believe her fanciful ghost story. Vera's inquiries indicate that Mr. Nuttel will be easily deceived and that she can have fun making the neurotic, unfamiliar man lose his nerve when Mr. Sappleton and Ronnie arrive home after hunting.