In what ways were the movements of American religion, reform and culture an outgrowth of the American revolution and American independence, and in what ways did they reflect qualities of American life reaching back to the Pilgrims?

can someone give me some ideas for this or aleast lead me the right way...

That's pretty broad, but I'd go with something along the lines of how important the concept of personal freedom has been ever since the beginning.

Look at people like the Quakers, who believed in equality and tolerance, and Puritans, who believed in things being strictly taboo such as sex outside of marriage, etc. and self-progression. By that I mean pushing oneself to be the best he can and those who are at the top of the chain are favored most by their God.