I think you misunderstand Uber. Most of its perceived value is in arbitrage between drivers' perceived and actual costs of car ownership: drivers mostly think in terms of wages minus cost of gas, ignoring all of the other costs. Given that business model, I doubt Uber is actually looking at buying these cars. They will presumably force drivers to buy or lease the cars themselves.

Currently both Uber and Lyft handle the task of vetting drivers and making sure there is a good experience for their customers. They organize and control the labor required for a good experience for the riders.

Think about a rider in a world where Lyft and Uber are both dispatching self-driving cars. What's the difference between the services if they're all using Mercedes S-Class SelfDrivers? The rider knows that all Mercedes S-Class SelfDrivers are the same experience. There's no question of if the driver is trustworthy or competent. Uber and Lyft would be providing the exact same commodity experience of sending a self-driving car to your location to then do your bidding in exchange for money.

In Uber's perfect world, yes. And Uber will do its best to hide the true costs of insurance, depreciation, regular maintenance, etc. from owners and lessors, just like they do today. It's worth understanding that Uber only works as long as it doesn't own any cars, or employ any drivers. If they switch over to owning some self-driving cars, they'll have to maintain and insure them.

In a hypothetical world in which we have fully autonomous vehicles and someone wants to compete with Uber, anyone who can afford capital investment in a fleet is not going to have much difficulty generating a customer base (and then they can have a mutually destructive price war with Uber).