Why can’t I find the Karin Kuruma

Most of the early game missions are triggered by phone calls from Simeon, Lamar, and one of Lamar's friends. These should start up at about level 4. As you level more options in free mode will appear.

I personally had problems with these events triggering automatically on day 1. Day 2 seemed to be better in that regard. Though be weary, there still seems to be issues with the servers not remembering everything you've accomplished.

The tracker puts a marker on the map, similar to the icon used for the Impound in offline player.

I believe the marker is called "Personal Vehicle" on the legend, so you should be able to find it fairly quickly.

Alternatively, if the marker isn't visible on the map, use your phone to call the insurance company and request a replacement.