I would use a SVG world map. search Wikipedia or Wikimedia, you may find the map you want in SVG format. hopefully, each country should be a separate object. then, see Processing's libraries, there's one to display SVG drawings.

to make each country clickable, you can use an image buffer and a simple picking method. draw each country in the buffer in a different color, then when the user clicks, check the color in the buffer, and you'll get the country. have a look to Processing Hacks > Picking if you want more info. hope it helps.

the simplest way is to create a Country class describing all the data you want to associate to the countries : name, shape, display color, buffer color, etc. Something like this :

Code:

class Country {
  SVG shape;
  int x, y;
  String name;
  color bufferColor;
} 

once you've created each country, you can put all of them in an array, and you'll get your world map. iterate the array and call shape.draw(x, y) to display the countries on screen.

you can treat wars/conflicts as arrays of countries. on mouseOver, check if the selected country belongs to one or another array, and see the other countries concerned by this war/conflict by iterating the array.