There are several ways in which the U.S. increased western settlement in the 1800's, but by far the most important action was the creation of the Homestead Act.
I assume you mean what challenges after they gained independence. They had many internal conflicts. This included fighting about religion. There were also natural disasters. There was the problem of transitioning directly from a dictatorship to a democracy.
Answer:
Peace Corps
Explanation:
JFK had this diplomatic approach of achieving the US's imagine and hegemony but spreading our ideals to developing countries. Therefore to create a "pure" presence in the world.
<em>On the Origin of Species</em> was a book written by Charles Darwin regarding the observations he made on his trip to the Galapagos Islands.
Hope that helped =)