Was the Second World War a war for democracy? In what respects—if any—was the American experience of the war undemocratic? Would you agree that FDR's Four Freedoms are still relevant today? Is the United States still an "Arsenal of Democracy"?

In my opinion it's undeniable that in many respects, World War II was, in fact, a war for democracy.
Because all major conflicts are based on complex issues and have multiple causes, the basic facts about any given war can sometimes be obscured. Various commentators have expressed cynical views about the Second World War, as they have about the U.S. Civil War and other events throughout history. Most people, however, would express the common-sense view that in some wars, there are clearly a right side and a wrong side. Both Nazi Germany and Imperial Japan were aggressor states that started the war and waged ruthless and genocidal campaigns against other nations and, in the case of Germany, against its own people. However imperfect our own countries have been internally, and whatever wrongs have been committed (and there are unfortunately many), Britain and the United States are democracies, and the Allied victory (in spite of the fact that the Soviet Union participated in it) was therefore a victory for democracy.
It was, however, an imperfect one. The defeat of Nazi Germany on the eastern front by the Soviets resulted in the Central and Eastern European states--Poland, Czechoslovakia, Hungary, Yugoslavia, and Romania--becoming satellite countries of the Soviets. But if the Axis had not been defeated, the entire Continent, including France, Belgium, the Netherlands, Italy, and most of Scandinavia, would have remained under Nazi domination or at least indirect control. So despite the fact that a large part of Europe came under Communist control, the outcome was still better (or less bad) than what would have resulted from a German/Axis victory.
Only the most cynical person could deny that the freedoms FDR spoke of are still relevant. Is the U.S. an "arsenal of democracy"? In my view this somewhat banal phrase is unhelpful. But whatever imperfections still exist (and there are many) in the U.S., Britain, and other countries throughout the world that have elected governments, could anyone possibly believe that a world dominated by Fascist or dictatorial governments would be better?