As another commented, it will be a very interesting optimization problem to figure out how to efficiently use the underutilized time of the fleet. There are a lot of things which are done at peak times now only because the owner of the car has to physically drive it there that could easily be moved to non-peak.
As for the uniform thing, you are right, but it can be restated in economic terms as the car being more expensive to use during certain times of the day -- so people will have an incentive to go to work in off-peak hours (which will be an option not available to everybody, but the more that do so, the less the premium cost will be) thus smoothing demand.
Exactly. The salient questions are whether, at the point of minimum demand during the day, there would be more unutilized self-driven vehicles than the current state of unutilized owner-driven vehicles, and if at the point of maximum demand, there would be more or less vehicles on the road than today.
Intuitively, the answer is "no" to the first question, since cars used for commuting in the morning and evening could be used for deliveries during the day.
I don't know about the second question, and this probably has more to do with shifting trips from public transit to self-driven cars (not cruising to avoid paying to park).
This research doesn't consider the reduction in parking demand, the reduced cost to park, the densification from reclaiming thousands of hectares of parking spaces, offsetting traffic of current delivery vehicles, etc.
The illusion of control is a powerful one, and I think many people will choose to own and park a personal car near to their work so that they can get in it and get stuck in traffic immediately, rather than waiting at work while the car returns through said traffic.
If they do, it will be theirs, not doing random shit for who knows who.