Some answers that your questions generated:
1. I'm thinking neutral evil wouldn't just conquer the world like chaotic evil, but subvert and subsume it. The daemons slowly took over the good-aligned churches and replaced those in power with daemon cultists. These high-ranking individuals then started a war between the churches, citing ancient religious feuds, depleting their resources. THEN the Horsemen of the Apocalypse were summoned to the mortal realm, and conquered the weakened nations.
3. Some random ideas: drow and dwarf strongholds deep in the underdark still resisting the daemonic conquest of the surface; elven kingdoms retreating to the Feywild and then squabbling amongst themselves; at least one nation protected by Asmodeus; and a Star Wars type "Rebellion" that resists the new rulers.
4. Stealing from WoW, the daemons want to consume the soul of the world.
5. The Four Kingdoms engage in civil wars and deadly politics now that the conquest is over. The Kingdom of Plaguemere is ruled by Apollyon, Prince of Flies. Plague daemons and diseased goatmen are at his eternal command. His forces seek to spread sickness among the ranks of the other kingdoms to take them over. If Apollyon gorges himself on the world soul, he will set himself up as Emperor of the Mortal Plane.

Just some thoughts. Hope you liked.