-Are facial rigs expensive when they “aren’t doing anything”?
No more than whats allowed for the actual character model’s rig. It’s a rig that can share the same skeletal pathway as the character keeping everything into a single channel including the animation sets. Clusters are way less expensive per vertex, easier to drive using voice or optical data, and it’s memory footprint is 1-1 no mater how many characters you add.
-Same question but with morphs. Do morphs even have a runtime cost while they’re just sitting there and not blending?
Of course. For each vertex that has a +1 it needs to be recorded as part of the morph progression and stored so although not moving it’s memory foot print can become massive and if for some reason the main target losses a vertex your entire morph chain will break. More or less if you have 70 shapes you have 70 times the load as you would have using clusters.
-Is there any documentation, any example of a AAA game that did randomized NPCs with facial animation, like e.g. Skyrim.
Well that’s trade secret stuff but I doubt they use morphing for anything other than the hero stuff but looking at it it seems to me Skyrim is just using the talking mail box approach. Cheap lip sync by taking the dialogue track, converting to rotation data and tada talking characters. In other words procedural and not keyframed.
To bug you one last time. 
Morphing animations is 1999 stuff and very expensive and high maintenance and extremal difficult to dive. It’s what Quake3 used to animate their MD3 player models and even though low poly account for the majority of the games over all foot print.
Clusters on the other hand are dirt cheap by comparison, can be driven procedurally, the animations reused on different characters, and keeps everything moving through the same animation pipeline with out the need for any special code or blueprints. Clusters is just another layer blend like aim offset.
If your looking for someone to tell you what to do I’ll say don’t use morphing for dialogue as it’s way to messy that takes a lot of planning when the ability to use clusters is already available as just another blend state.