You can select that shape in Pages v5.6.1 and press command+C to copy it to the clipboard. If it is a composite shape, select all components, and then from the Arrange tab, select group. Now you can perform the first sentence.
Launch Preview (Launchpad : Preview), and press command+N to open that shape from the clipboard. You will now have the shape on a transparent background. Export it in your favorite, mainstream image format (e.g. png, tiff, jpeg, pdf, etc.) and save it in a new folder (Pages) in your Pictures folder. You can now drag/drop that image into future pages documents.
Or, you can maintain a Pages template document strictly for these vector images, and open that separately to copy/paste images into your main document.
Pages '09 v4.3 allows one to add images and clipart to its Media browser, where one can see them all as thumbnails. Unfortunately, this capability was not added to Pages v5.