Car-mode is really nothing else than pressing the fullscreen button on top of the device in the music view.

The current playlist is visible in the playlist view (2nd icon from left on the menu panel). There you have by default a list called "Queue". This is not really a playlist, but a queue. The queue doesn't get saved across sessions, and played items are removed from the queue automatically.
You can press the [+] button in the toolbar to add new playlists. The currently selected playlist is the target playlist when enqueuing media. Playlists are saved across sessions and can be reordered by dragging the items.

If you have ideas of how to make this simpler and easier to understand for users, I'm interested to hear them. Usability is a top priority.