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In Shirley Jackson's short story, "The Lottery," I believe that had Tessie Hutchinson told the story in the first person, the overall difference would have been a decided lack of the surprise, shock and denial on the part of the reader as the story stands, for Tessie would have shared her inner thoughts, providing a context for the seemingly casual gathering of the townspeople.
When Tessie Hutchinson first arrives, running a little late, there is no sense of an impending threat. Because we do not know what she is thinking, we get no warning. She does things any woman might do when rushing from the house: she chats amiably with those around her as she slips in, probably panting a little, while she dries her hands on her apron. If we were able to read her thoughts, she might well be wishing she could have slipped away unnoticed; she might be one of the people who is beginning to doubt the validity of such a practice; before knowing how she reacts at the end of the story, her personal viewpoint might well express serious concern for her family members, and she might even recall those they have known and lost in the past.
Soon after, the Hutchinsons are united. Mr. Summers cheerfully jokes with Tessie about just making it in time, and Tessie jokes back. Had we the opportunity to hear Tessie's thoughts, I would think that she might express a feeling of dread, as she might every year at this time; she might also very much resent Summer's ability to joke at a time like this. Summers is described as a jovial man, but under the circumstances, humor hardly would seem fitting. This might anger her.
With careful manipulation of Tessie's thoughts, the ending of the story still might be a shock, but the little clues that Jackson leaves along the way would probably be unnecessary or lost.
The idea that "if it doesn't affect me, it isn't a problem" is seen as soon as Tessie complains about the process after her husband chooses "THE" paper. Someone suggests that Tessie be a "good sport." If we had been reading Tessie's first person point of view, we would have realized much sooner why sportsmanship would have been the last thing on her mind.