And then you remember that as part of the passenger safety case for driverless taxis, there will necessarily be cameras and microphones and the ability to lock the doors and redirect the taxi to the nearest hospital or police station, right?
When we were building the Heathrow Pod[1] -- which is effectively an autonomous taxi system -- this was an objection that people raised all the time. In practice, it took approximately zero instances of bad passenger behaviour for people to catch onto the fact that the interior of an autonomous vehicle that can deliver you non-stop to airport security is really the last place on Earth that you'd want to engage in anti-social behaviour.
Presumably not if you own the car. Sex in public (including in buses, subways, etc.) is already illegal in many areas, and cab-company equivalents would presumably get to set their own rules as they do now.