When the narrator brings Doodle to Old Woman Swamp, what is the significance of nature as described in the passage, and how is nature connected to...

[The original 6 questions had to be reduced to one main one as this is standard procedure. Please re-post the others separately.]

Whenever the brother feels a connection to Doodle, a bond begins to form, and when Doodle shares his love of the beauty of Old Woman Swamp, there is a new, closer relationship formed between them.

Earlier, the brother pays attention to his baby brother only when the boy learns to crawl and is...

[The original 6 questions had to be reduced to one main one as this is standard procedure. Please re-post the others separately.]

Whenever the brother feels a connection to Doodle, a bond begins to form, and when Doodle shares his love of the beauty of Old Woman Swamp, there is a new, closer relationship formed between them.

Earlier, the brother pays attention to his baby brother only when the boy learns to crawl and is brought out to the front room as one of the family. "For the first time he became one of us." Still, Doodle is a "burden" to the brother as he must pull the frail boy around in a go-cart. Then, one day when he takes Doodle to a favorite spot of his, Old Woman Swamp, Doodle becomes so emotional about the beauty of nature in this pristine area that he cries and remarks, "It's so pretty. So pretty, pretty, pretty." 

It is at this point that Doodle connects again with his brother because they share a deep love of nature together. Returning to this favorite location in the fair weather, the brother gathers all sorts of wildflowers and they weave them into necklaces and crowns, wearing them in sheer delight of the beauty of nature.
But, in the midst of this halcyon experience, the brother narrates that 

...pride is a wonderful, terrible thing, a seed that bears two vines, life and death.

Now, when they go to Old Woman Swamp the brother, in his "death vine" of pride insists that Doodle learn to walk. When Doodle finally accomplishes this skill, the brother shows Doodle off to his family.

These passages that describe Old Woman Swamp hint at Doodle's strong connection to nature. For, much as in the natural world there is a similar impermanence and transitory quality to frail, small boy; however, this frailness is a quality that in his selfish pride the brother ignores, a psychological state in him that presages the tragic actions of the future as he pushes Doodle to accomplish more physical skills.