When did the idea of countries first appear? Who established the borders?

To answer your first question you would have to define what you mean by country. There were groups of people with governments and somewhat similar languages since at least the time of the Mesopotamian civilizations of Ubaid, Sumer, Akkad, Assyria and Babylon. If you see a country as having a degree of democratic rule, there were the Republic of Rome and the city-states of Greece since the [6th century BCE.] (http://www.ushistory.org/civ/5b.asp) There is a interesting book called Peasants into Frenchmen, written by Eugen Weber, where he argues that in France, traditionally seen as the first modern nation, there was little identification with a French identity outside of major cities, into the 20th century. I don't have the book in front of me and therefore cannot quote it accurately, but he gives a statistic at some point to suggest that a staggering percentage of the "French" did not speak "french" in 1910.

To answer the second part of you question, the history of the borders we see today have to be taken on a case-by-case basis. For example, many African countries and their borders are their result of European colonialism and the Berlin Conference of 1884-5 where the continent was essentially divided between European powers. Throughout the 20th century, areas that were once African colonies won their independence but kept the same borders for the most part. Similarly in South America borders are, for the most part, legacies of Spanish and Portuguese colonial rule..