What should be the causes of a civ's development and downfall? Should it be on a fixed timer, as MDF said?
The causes of the development of a civ could be the
Should civilizations be able to balkanize? If so, when and why?
Balkanization should happen when much cultural drift happened, drift helped by huge distances or obstacles such as mountains or oceans, along with the presence of another civ to influence.
What should trigger the development of a completely new civilization during worldgen? Should the ruins of a dead civ be able to foster the growth of another group, or do they need to be conquered outright?
When enough drift happened - about this, could we envision future public entities (states and asimilated statuses) separated from civilisations, so that one state might have several civilizations (IRL, Switzerland has the French, German and Italian civs) and a civilization might be separated in several states (Greece, which was divided in several cities and kingdoms)? -, a new civ should be created.
And dead civ can serve to create another one - see the Classical culture after 476.
Should a player adventurer be able to conquer sites in the name of another civilization?
Yes, as a
conquistador, or even for himself.
Should a player fortress be able to form its own government/send out settlers/etc. and separate from the parent civ?
If they don't want to pay their taxes, then yes.
Should civil war's frequency increase in civs liable to nationalism and balkanization?
Yes, because they want to be separate.
Where should mythgen fit into the role and development of the states?
Gods and other deities could interviene in the creation of some civs, and rulers could claim to descend or having been granted their rule by deities.