How did Christopher Columbus impact North America's culture, demographics, religion, and relations with other regions of the world?

We tend to overestimate the importance of Christopher Columbus as an individual.  Columbus himself had very little impact on any of the things you mention in your question.  He was merely the first European to lead a voyage that resulted in colonization in the New World.  He never even saw the continent of North America.  Rather than saying that Columbus affected North America, we should say that the Europeans who came after Columbus affected North America in the following ways:

• Demographics.  In much of North America, the Europeans killed most Native Americans or, at the very least, moved them onto small pieces of remote land.  This paved the way for much of North America to be inhabited by Europeans and their descendants.  In Mexico, the Europeans did not kill as many natives and, instead, mingled with them, creating a country that is most mestizo.


• Culture.  Because so few Native Americans remain in the US and most of Canada, we can say that their culture was basically destroyed and replaced by a culture based on European culture.  In Mexico, a hybrid culture blending European and Indian influences arose.


• Religion.  This is a part of culture. Native American religions essentially disappeared over most of North America, even in Mexico.  In the US and Canada, Europeans settled most of the land and were barely affected (if they were at all) by Indian religions.  In Mexico, Indian religions have influenced Christianity much more, leading to celebrations such as the Day of the Dead.


• Relations with the rest of the world.  Before Columbus, the Native Americans had no relations with other regions of the world.  After the Europeans came, North America became a major part of the world as a whole, leading to the situation today in which the US is the most powerful country in the world.