1) I actually think self-driving cars are moving faster than expected. Ten years is still a pretty reasonable guess, considering the pace of governments and the auto industry, but we're closer than I thought we'd be by now.
2) Uber will use self-driving cars, probably exclusively as soon as it's legal.
Uber wants to be the internet of the physical world. With the internet, information could travel anywhere with the tap of a finger. Uber wants the same reduction of friction for objects and people.
The problem for Uber is it's already easy to poach drivers from Uber. Drivers don't care if they drive for Lyft or Uber because the payouts are pretty similar. I've met drivers who switched between both.
When cars drive themselves, Uber will have to become even more competitive to stay on top. The cost of building an Uber-like fleet will be no more than buying the hardware.
Remember how hosting companies proliferated in the 90s and early 00s? Until AWS and similar PaaS options, the hosting space was incredibly fragmented, and the margins were awful. That's what Uber has on the horizon.