I tend to sympathize with Framton Nuttel, mainly because he doesn't want to be there in the first place. I would hate to be in his situation, having to present a letter of introduction to a houseful of total strangers. It seems like being a beggar. I don't know how common that sort of thing used to be in Saki's time, but it seems like a weakness in the story that a nervous, introverted man like Nuttel would show up at a country mansion with a letter of introduction. What would he be expecting of them? What is the letter supposed to get him? Would they invite him to one of their big parties or to a dinner where he could meet some of the local gentry. If he doesn't enjoy meeting the strangers in this house with the open window, wouldn't it be even more unpleasant to meet more strangers at larger social functions. Maybe his sister is an extravert and enjoyed meeting everybody in the region when she was staying at the rectory, but Framton will never be like her. Neither would I!
I agree with #3. Nuttel serves a limited purpose of being a susceptible victim that Vera can prey upon. Like a master huntress, she quickly sizes up Framton and then pounces swiftly upon his weaknesses with a satisfying, if rather cruel, conclusion. He is most definitely a flat character whose only function is to suffer from a nervous disease that makes what Vera does to him all the more darkly humorous.
To me, Nuttel is in most ways a non-entity in this story. In other words, I feel that he is unimportant to the story. To me, the story is really about Vera and her imagination. There is nothing special about Nuttel that makes him important. Any person who is gullible enough to believe Vera would do. The story is about Vera's ability to make up stories (and persuade people of their veracity) on the spot that really drives this story.
We can see that Nuttel is not really important at the end of the story. There, Vera is going to (it seems) fool her aunt in much the same way she fooled Nuttel. She is the real story here, not her "victims."
Readers' attitudes toward the characters of a narrative are largely determined by the tone of a story; that is, the attitude that is taken by the author toward the subject. In Saki's "The Open Window," the author's tone is rather matter of fact as the narration is third-person objective. However, as the story continues, Saki's typically ironic tone emerges as he pokes fun of Framton Nuttel's gullibility. With Vera's story, Saki cleverly pits imagination against reality, triumphing over Nuttel and the reader both with a clever frame- within-a-frame story.
Since readers are often defeated by Saki's ironic wit, they tend to view Framton Nuttel as gullible as they have been, and, perhaps, a little worse as he has nervously worried about flattering the niece and pleasing her and, then, fled from the room in fear when the horrifying conclusion to Vera's tall-tale occurs.