Has anyone ever noticed if the Choose Successor in Lydes I & II, Investigate Hunter Fell, or any other completed war table operations have disappeared from their war table. I do not remember if I did these, but I am about to finish Demands of the Qun and want to complete these first (if I haven't already).
The two quests you mention are "provided" by the Ben-Hasserath. They will or will not disappear after Demands of the Qun, depending on the choices you make during that quest. Specifically, they will disappear if:
you choose to save the Chargers rather than the Qunari dreadnought.
If you have not yet gone to the Storm Coast to start Demands of the Qun, they should be available.