Palettes can be exported from the website and from the CC Capture.
Color libraries are available from the website only.

Exporting Palette from CC Capture.

If you need to display a palette content while the instrument is in measurement mode hit the "Reset" button or click on the palette name (left-side).

Your CxF file will be downloaded to your Export Folder (CxF subfolder) - if not defined system will ask you where to download the requested file.

Read also:
Exporting CxF from the Color Inspector website interface.