FWIW, that's what is so dangerous about AI, though? Not that it will necessarily want to kill us, or even that it will necessarily be able to "want" to do anything, but that we will get in the way of its incessant drive to optimize the efficiency of the paperclip factory that prompted it on a whim before leaving for a long weekend.
Sure but you can totally contrive scenarios to give the appearance of what you described without really doing anything notable.
What matters is scale. Did it deploy a novel zero-day exploit to overcome a problem? That's alarming. Did it kill a disruptive process? Pretty normal troubleshooting step.
Exactly, intelligence is limited by cost and physical constraints just as much as anything. That's the thing that seems to always be missing from the run-away singularity discussions, it's treated like a perpetual motion machine.