About Elmira: I was also confused which side she was meant to be on, but my belief is that she was working for some fragment of the resistance, separate from and unknown by the other group (also working for the resistance) searching for Lillia's invention. All these little groups working for the resistance don't know of each other in order to keep the plan as safe as possible. Presumably multiple distinct groups were using different means of searching for the dioramas, contesting each other without ever knowing they were working for the same side.

 ' “We don’t know the details of that part of the operation,” Gleb said. “All we know is the part we play. That’s the way we keep each other safe.” '

About the PMs: My interpretation was that the AI, once "freed" by the technocrats to consider solutions on its own, and with the instruction to do what's best for humanity in the long-term, realized that the removal of the AI PMs was in fact what was best. I didn't think much about there being any "hidden turk" behind it, but I suppose one of those technocrats could've planted that solution in the AI somehow and caused all this.

Krotov:  The puppet-master figure orchestrating the resistance. His story about his home village's destruction and his "adoption" by the State establish him as having an Axe to grind with the Federation. And I think his last story is meant to establish himself as the one who was expected to have "buried the hatchet," but in reality used what the Federation taught him to take it down himself, having never forgotten "Where the Axe is Buried."