1. robo-taxi companies will self-insure. Insurance is just spreading the risk. If you have a fleet of 10.000 cars, self-insurance will be cheaper
2. by "death" he means "significant decline", not "disappearance". A company that buys 10.000 cars has a purchasing power that a single customer doesn't. They can dictate the specs to a car company and they can pit several companies against each other to get the best deal. They can even co-design the cars for their own metrics (e.g. fuel efficiency, reliability, maintainability is super important for someone who has a large fleet).
Car companies will have no choice but to play ball, some of them will go bankrupt and the remaining will service a much smaller market.
3. You assume that self-driving cars need a lot of new regulations. They don't - they just need to be allowed on the road. The rules have already changed in Nevada in California. When the technology is proven, the states will have a hard time justifying not allowing technology that is proven to save a significant number of lives.
4. robo-taxi companies will bring repairs in-house or outsource to existing companies. Again, they'll have upper hand in negotiations due to providing a lot of business and the overall market for repairs will shrink dramatically. Google could bring all their statistics knowledge to predicting what and when will fail and use the past data to improve the parts that fail the most.
5. not sure what you're driving at
6. agreed, probably overstatement on the author's part
Google (or some other robo-taxi company) doesn't have to make their own cars, they'll have enough pricing power to pit multiple car manufacturers against each others to get the best deal, drive down the margins etc., just as Apple does with iPhone parts manufactuers (where Apple gets most of the profit from the phone).
They can self-insure - the liability never goes away but will be manageable from revenues.
As to people who insist on owning a car - most of them will change their mind because of price. If you leave college with $50k in student debt, are you going to spend $10k on a new car + monthly insurance + gas + cost of garage ($100/month in San Francisco if your apartment doesn't already come with it) + hassle of owning a car or will you pay $100/month for much more convenient car-as-a-service deal?