First the easy part: you can delete a favorite by tapping the star in the info panel (or the detail screen) of the selected favorite. It’s an on/off toggle.
Another way to delete favorites (either pins, pois, routes or tracks) is to go to Main (left) menu » Favorites and tap the Edit button in the upper right corner. Now you are able to select multiple favorites. To delete the selected favorites you can tap the trashcan in the lower right corner. To answer your question about groups: instead of deleting the selected favorites you can add them to a group by tapping the folder button which is next to the trashcan (placed at the lower middle).
This will also work in the Favorites Per Type sections: My POI, My Pins, My Routes and My Tracks.