Nothing is stored on your phone, everything is on some Waze-server.
You can see your drives when you open the editor on the waze-website (www.waze.com
in the US and Canada, world.waze.com everywhere else). Click the "My Drives"-tab.
Currently you can not get any statistics on your drives. I wonder what you want to use those for - if one route is faster than the others this route will be your preferred route for this moment. Waze routing adjusts by the minute and there is - by design - no way to store one particular route. As of the "learn my preferred route"-option: it is misnamed and should be called "learn my destinations".