There a multitude of easy fixes for this. I believe in London if you drive into the center, you have to pay a road fee or something like that.

Seems to me that this would fix the issue.

Also, I think that self-driving cars will have people sharing cars rather than owning one themselves, this will lead to fewer cars being owned overall, but not necessarily leading to less traffic since when you own a car it mostly just sits in your parking space.

Fewer cars means that those self-driving cars will probably be always on the road, which won't lead to any traffic savings.