That's one hell of a detailed story. Don't believe it.
https://en.wikipedia.org/wiki/Conjunction_fallacyAbout nanotech: if we have nanofactories, nanoreplicators shouldn't be far. Beware the gray goo accident.
As for AI, it will probably go from "quite dumb" to "way smarter than we are" in a relatively short time. At that point, everything else will be moot, because the AI will do pretty much what it wants (what its programming tells it to do) and we won't be able to stop it. Let's hope (or ensure that) its "wishes" are the same as ours.