As a part of setting what time of year does the author use to demonstrate the theme in nothing gold can stay. nature’s first green is gold, her hardest hue to hold. her early leaf’s a flower; but only so an hour. then leaf subsides to leaf. so eden sank to grief, so dawn goes down to day. nothing gold can stay.

Well, it's fall of course.

the sentence that avoid faulty coordination is:

culture, which is well represented in philadelphia, plays a major role including theatre, music, and the visual arts.  

faulty coordination occurs when the writer gives equal importance two different ideas (clauses) which in fact are not equivalent. in order to correct a misplaced clause or idea, the writer can place less important or emphatic ideas in a relative clause as in the previous sentence.  

i think it is called the president's cabinet.