No, you do not need an API key. It is only used for ThinkGeo Cloud services.
The Z/X/Y.png setup mimics a TileCache, not a datasource. Because of this, it might be better to just use the DWG file:
CadFeatureLayer layer = new CadFeatureLayer(@"myfile.dwg", CadStylingType.EmbeddedStyling);
LayerOverlay layerOverlay = new LayerOverlay();
The reason to use this over the images is because it’s more efficient and since the tiles are static, you would have a lot of issues showing the images when using even the slightest different ZoomLevelSet or MapUnit.
For example, let’s say that those images on Z=16 were created to a world scale of 1:10000. In your map, you need to make sure that ZoomLevelSet.ZoomLevel16’s scale is exactly 1:10000. If it were 1:20000, you would have a very misleading basemap where the perceived scale would be double it’s actual scale.
My best advice is to keep it in a vector format (dwg, shapefile, or otherwise), or utilize georeferenced raster formats such as GeoTiff. And if you want to have Z/X/Y.pngs, use them only as a TileCache of a georeferenced datasource.