All snakes are different. Some are fine with handling right when you bring them home, others need some time to realize that they are safe and not in danger. If you start handling a shy snake too soon, the snake might not eat. Best to get the snake eating first, then start with some handling.

As far as what to do with the snake in the car.. I like to use snake bags, then put the snake in a secure tub. Keep the snake out of direct sunlight and it should be fine as long as the car isn't super hot or super cold. The tub should help insulate if its a little colder.

When you get home, just take the snake out of the box/bag/whatever and put it in its new home. You don't need to let the snake get out on its own unless you think it might bite you for some reason. This isn't really a problem with ball pythons though since they are so gentle. I let my tree snakes leave the container on their own just because I don't like to mess with them needlessly, especially when I first bring them home.