Regarding driving through car parks. Well, I show up daily at a coffee establishment in front of a mini-mall. There is 90 degree parking on both sides of the access 'street' which bears no name yet is treated as a street because it is open at each end. 90% of the folks there ae slow and careful, but those who treat it like a street are not on a schedule and there are near misses all the time.

Come to think of it, there are parking areas where people drive through at street speeds as well.

So yes, pedestrians have priority. But at their peril!

And I just remembered that horror story about the kid in a pickup truck who drove into about ten motorcycles, and killed seven. Being right doesn't lead to staying alive.