Patch 1.3 changed it so that when you have spent all of the Quest Points given for the Ambition it now says that you have infinite QP instead of 0QP. This means you can continue to quest with your heroes, although I'm pretty sure you can't gain any more credit for achievements or ambitions.
When I did Imperial Domination I annexed all the kingdoms on the map and was confused as to why it didn't count me as having annexed all of the kingdoms. Turns out that you need to go to the Village Shoppe and buy Map to Effenmont and Map to Gastobury. Once you have the maps then click on the ship and go explore the kingdoms. Any hero can do this. Once that's been done Effenmont and Gastobury will appear on your map and you can annex as normal.
Hope this helped.