To obtain line contours rather than solid regions, go to View>Contour Options (or right-click and select Contour Options from the popup menu) and change the Contour Mode to Lines. You can experiment with the various contour options (Auto Format, Range, etc) to obtain the desired contour values.
Change contours appearance in Contour Options dialog
As for adding labels, unfortunately it is not possible to add Contour Labels or Text Boxes to the 3D View. The only thing we can suggest is to maximize the 3D view, obtain a screen capture, import the screen capture into an image editor and add labels in the editor.
You can try different display options as well (e.g. turn off the display of the soil column in the sidebar view controls).
In addition, if you right-click on a line query there is an Export Data to Excel option, which exports all of the data along each vertical string which makes up the line query.