This question could take books to adequately answer. The four centuries between 1400 and 1865 saw tremendous changes in all areas of life on what is now called North America. Here is a quick overview of each part of the question.
With the voyages of Christopher Columbus, new cultural groups settled in the Americas. These cultural groups were very different from the native population. Ethnic groups that settled in the New World were English, West African, French, Spanish, and Dutch. The European groups brought new languages, class systems, religions, and customs. Africans were subjected to chattel slavery and had no rights. There was a vast exchange of agricultural goods and animals between the natives and Europeans.
The greatest change in terms of economics was the introduction of a cash system by the new settlers. Surplus agriculture replaced the hunting and gathering that was practiced by native populations. Mercantilism, a precursor to the American capitalist system, was established in the 1500's in the new colonies. By the late 1700's, the North had moved to an industrial economy that relied on manufacturing. The South operated a cash crop economy based on agriculture.
The Europeans brought Enlightenment ideas with them to the Americas. Ideas like individual freedom and representative government were established in the colonial governments and became the cornerstones of American independence and constitutional government. A political party system had taken root in the United States soon after the establishment of a Constitution. The Native American populations were marginalized politically and culturally.