Ok well you wait for 20 minutes for a car every morning or operate on some pre-set schedule. I'd like to keep my own schedule.
That's perfectly fine. But it will probably be more expensive than on-demand or pre-scheduled transportation services once self-driving cars are a reality.
Yes I would expect insurance for autonomous cars would drop to around $50 a year since the human is no longer responsible or able to control for anything that happens in a truly autonomous car. Insurance will protect the value of the property and nothing that may happen with it. Passenger not liable.
It's not yet clear how liability will be distributed. Clearly liability will be held by somebody. In my opinion the most likely scenario is that the operator of the vehicle will take liability for its operation and will purchase insurance commensurate with that liability. The operator is whoever is commanding the vehicle. If you own your own self-driving car and tell it to drive you from point A to point B, you are the operator. If you hire a self-driving Uber, you tell Uber to take you to point B and Uber tells the car to drive you to point B, Uber becomes the operator.
Self-driving car insurance will be cheaper if the safety is higher with self-driving features, which seems likely. The insurer would hold the manufacturer of the vehicle liable in cases of gross negligence, but not in the situation of ordinary crashes which are a statistical certainty and included in the insurer's calculations. Insurers don't require perfect safety, in fact perfect safety would put insurers out of business. They just calculate a risk, and bill enough to cover their risk plus overhead and profit margin.
If the laws change so that vehicle operators do not need to accept liability for a self-driving vehicle they are operating then the manufacturer would be liable and the insurance cost would be reflected in the purchase price of the car.