There are only 4 types of quests from NPC factions:
- kill a enemy army
- kill a marrauder spawner (wich currently does not have an army)
- build something in your cities. This is a construction project, right next to the building building
- research some tech. It is auto queued on accepting, in 99% of all cases under social. However if you pick something else, you got to re-select it via the selection box at the bottom