Are the apps opened in CarPlay still running after disconnecting phone from the car?

You don't ever need to to force quit apps when you're done with them.
Evidence provided by Apple themselves a few years ago

If you don't tell a SatNav you've finished your journey*, then it will keep actively navigating.

Otherwise, just unplug your phone & off you go.

*Some of them insist on continuing to navigate to some pre-determined spot 50m from where you actually wanted, so until you pass through its destination point it will still keep on trying.

Incidentally, apps can be told from settings not to be allowed to use your location &/or track anything whilst not active, & Google apps can also be told from your Google account not to track you.