While sudden braking definitely contributes to it and is dangerous, this is mostly the fault of the drivers crashing into the self-driving vehicles even if they stopped without a good reason. And those vehicles are rather obvious, i.e. the driver following could have known that tailgating them at an unsafe distance is an even worse idea than with human drivers.
To your second point, nothing on those vehicles says "warning, no human in control" so I'm not sure how obvious it really is.
You absolutely can; it's what you're supposed to do if a toddler runs out in front of the car, for example. Barring malfunctioning brake lights, if you rear end a suddenly stopping vehicle, you were at fault for following at an unsafe distance.
Most legislation about this (example: https://codes.findlaw.com/ca/vehicle-code/veh-sect-22109/) says stuff like "when there is opportunity to give the signal". Screech brakes, then signal.
Kid in the street is a reason to stop suddenly
But it's pretty hard to enforce just for the reasons you mentioned. "I saw something on the road" is a fairly bullet proof defence which nobody can counter.