What method or methods does the author use to develop the main idea, and how do the methods serve the author's subject and purpose? How does the organization serve the author's subject and purpose?

This is only a short-answer space. You are asking a lot here. The author uses understatement and foreshadowing a lot to develop Paul's chraracter. Cather also uses symbolism to great effect in this story. Flowers are a continual motif, expressing Paul's character and his views of life. The red carnation Paul wears to meet with his teachers is to them a sign of his outlandish and insolent attitude. It is described as "flippantly red" and "scandalous." Paul also wears" violets in his buttonholes and dismisses those who do not do likewise as mundane. At the Waldorf, his grand suite is not complete without flowers, and he notes with awe the artificial beauty of cut flowers in the glass cases of New York flower stands, "against the sides of which the snowflakes stuck and melted." When Paul ventures to the railroad tracks to kill himself, he takes a wilted red carnation from his lapel and buries the flower in the snow. Expensive, extravagant, colorful and ephemeral, flowers represent Paul's desire for beauty in what he sees as a gray world. They also symbolize Paul, who, like flowers in winter, is out of place. The flower-killing snow Paul sees on the train to New York and by the railroad tracks at the story's end provide a stark contrast to the bright flowers Paul surrounds himself with.