What is the American Dream? How is it connected to the play "Death of a Salesman"?

I moved your question to the "Death of a Salesman" group since I didn't see any relationship to "The Scarlet Letter."

The American Dream has several interpretations.  One of the most common deals with economic success --- the house, the yard, the car.  The Dream says that we all the "right" to this dream, although I think the dream, if it has economic interpretations, only refers to the fact that these things are possible for anyone who wishes to work for them.  For Willy, the dream is related to this.  He has the home and the car, and dreams of being the success that the old salesman on the train was.  He thinks that the recognition and the things will make him happy.

The other possible interpretation of the American Dream is that we all are free here to seek the life that we wish.  We have all the freedoms of the Bill or Rights.  It does not necessarily entail economic success, just the freedom to be whatever we wish.  This is not the sense in which it is used in "Death," but is an important interpretation of the Dream.