The CPs acquired by a victory are missing from the battle report, so it is only logical not to have a clear understanding of the conquest logic.
Normal difficulty provides X CPs when victorious, Hard difficulty X+Z and Nightmare difficulty X+Y. Obviously, the harder the difficulty, the more CPs are acquired. PvP will also give even more CPs.
As we are testing the conquest cycles and the conquest system in general, the "containers" for each region have a very small value, meaning that someone who has a free day or two, could change the balance on the World Map. When the game goes live, this will change.
Regarding the extra difficulty, "Easy", it is something that we are seriously considering. Easy Difficulty would not provide any CPs, but it can be a training ground for the users' units. It will have a handicap, while Normal, Hard and Nightmare won't.
Admittedly, we want to tinker with the logic behind the number of units involved in a battle and the CPs acquired in the case of a victory. We are working on it.
Good feedback guys!