Considering setting as character. How does nature in “A White Heron” interact with the characters of the story? What are the two most important interactions between the character and nature? Why?

The natural country setting of the story is, apparently, what has enabled Sylvia to grow and thrive. Her grandmother believes that

There never was such a child for straying about out-of-doors since the world was made! Everybody said that it was a good change for a little maid who had tried to grow for eight years in a crowded manufacturing town, but, as for Sylvia herself, it seemed as if she never had been alive at all before she came to live at the farm. She thought often with wistful compassion of a wretched geranium that belonged to a town neighbor.

Sylvia, it seems, could not grow while living in the city, and it was this change in her home—moving from the manufacturing town (which we might imagine to be dusty and polluted from this description) to her grandmother's farm—that actually has allowed her to blossom (unlike the flower at her neighbor's in the city). Sylvia's name even comes from the same root as the word sylvan, which refers to one who frequents the woods or forest. She is often compared to natural objects, like flowers or stars. When she is forced to interact with the strange hunter, "She hung her head as if the stem of it were broken." When she climbs the great pine tree later in the story, her "face was like a pale star." It is as though Sylvia and nature are kindred spirits, as if she were something more natural even than the rest of us—certainly more "natural" than the hunter, who seeks to preserve by killing, whereas Sylvia seeks to preserve by protecting.
The most important interaction that a character has with nature in the story is when Sylvia climbs the pine tree to look for the heron's nest.

She stood trembling and tired but wholly triumphant, high in the tree-top. Yes, there was the sea with the dawning sun making a golden dazzle over it, and toward that glorious east flew two hawks with slow-moving pinions. How low they looked in the air from that height when one had only seen them before far up, and dark against the blue sky. Their gray feathers were as soft as moths; they seemed only a little way from the tree, and Sylvia felt as if she too could go flying away among the clouds. Westward, the woodlands and farms reached miles and miles into the distance . . . truly it was a vast and awesome world.

Sylvia seems to be in awe of all she sees, especially the natural splendor of the earth from so high up with the dawn breaking and the birds soaring. Later, it is this experience with nature that seems to prevent Sylvia from telling the hunter where the heron's nest is, despite how much she longs to please him.
The other most important interaction is the first one when Sylvia attempts to find Mistress Moolly, her cow. It is here that we initially learn of Sylvia's love for nature. One of the first things we learn about her, as she drives the cow home, is as follows:

[Sylvia and the cow] were going away from whatever light there was, and striking deep into the woods, but their feet were familiar with the path, and it was no matter whether their eyes could see it or not.

She is described as animallike because her connection to the natural world is so strong.