Yes, I mean to say civil war is a subset of insurgency. Insurgency is simply violence against established authority. Civil wars are always large insurgencies (hence the "war").
Not sure I agree with that. How do you define "established authority?" Who, for example, was the established authority in the Russian civil war? What about cases where the insurgency gains the upper hand and becomes "established" but elements of the old regime remain and continue to fight? At what point to they change from being the "established authority" to the insurgent?