how are the setting and smybols connected?

This is seen throughout the story. I'll concentrate on the beginning because here the setting and symbols are so connected. This opening chapter of the main narrative introduces several of the images and themes within the story to follow. These images will recur in several settings and serve as metaphors for the underlying conflict.

In the manner that Hawthorne describes it, the prison embodies the unyielding severity of puritan law: old, rusted, yet strong with an "iron-clamped oaken door." Puritan law is coated, in this account, in the rust of tradition and obsolete purpose. But despite the evolution of society, the laws have not kept up. As a result, the door remains tightly shut and iron-clamped. It seems it will take a superhuman force to somehow weaken the mores that control the society in which our story will take place.

With the reference to Ann (actually Anne) Hutchinson, the prison also serves as a metaphor for the authority of the regime, which will not tolerate deviance from a prescribed set of standards, values, and morals. The rosebush itself is an obvious symbol of passion and the wilderness, and it makes its most famous reappearance later when Pearl announces that she was made not by a father and mother, or by God, but rather was plucked from the rosebush. Roses appear several times in the course of the story, always symbolizing Hester's inability to control her passion and tame it so that she can assimilate to Puritan society. Pearl too is marked by this wildness.