Charlotte told Wilbur she couldn't go to the fair with him because she was dying. She had laid her eggs and knew she would not survive for long after that.
Wilbur was worried at the fair because he was facing the possibility of being sold and separated from his friend Charlotte the spider. He was also nervous about competing in the pig contest and unsure if he would win.
Charlotte couldn't go to the Country Fair with Wilbur because she was too big to travel outside the barn. She needed to stay back and protect her eggs instead of venturing out with Wilbur.
Charlotte the spider decided to go to the fair to save Wilbur the pig's life. She knew that Wilbur was in danger of being slaughtered, so she used her web-spinning abilities to write a message in praise of Wilbur to convince the fairgoers to spare his life.
The word Charlotte spun at the fair was "some pig" which saved Wilbur's life by convincing the farmer to keep him.
Templeton delivered news of the county fair to Charlotte and Wilbur, specifically regarding Wilbur's impending participation in the fair's Zuckerman's Famous Pig contest. Templeton's greed for rewards motivated him to share this news, as he hoped to benefit from any potential winnings or food at the fair.
Uncle was the pig that had the stall next to Wilbur at the county fair.
Wilbur went to the fair because he won a special prize for being the best pig in the county. He went with Charlotte the spider to celebrate and enjoy the festivities.
Charlotte felt that she should not go to the fair with Wilbur because she needed to stay behind to take care of her eggs and watch over them as they hatched. She knew it was important to fulfill her role as a mother spider.
Templeton (the rat) helps Charlotte find words, Charlotte writes words on her web to save Wilbur, the sheep tells Wilbur and Charlotte that Wilbur is going to dye so everyone gets ready to save Wilbur, and the goose comforts Templeton to go to the fair to help Charlotte write words on her web.
Charlotte spun a web with the word "Terrific" above him, which attracted attention and saved Wilbur from being sold. This act of creativity and kindness helped revive Wilbur and changed his fate at the fair.
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I don't think it has a name... I think it is just 'The Country Fair'