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Nope. No need for images. They just know about the content and link to it. The cached HTML shows they store a copy (or cache) of the HTML though. I could be wrong about the images but that would exponentially increase their storage needs so it seems unlikely.

You can't get their domain validated in your Google Search Console account (unless they add you as a user to their account), however there is a workaround more or less described here: Getting CDN images indexed with Google In short: If your image is for example on https://12345.maxcdn.com/images/directory/subdirectory/image-filename.jpg You can add a CNAME (alternate domain name) to make the URLs formatted like this: http://images.yourdomain.com/images/directory/subdirectory/image-filename.jpg After that you can add "images.yourdomain.com" as a verified domain in Google Search Console and treat it as a new subdomain, incl. sitemaps etc. Hope this helps

What software system is your website built with, Archie? If it's a Content Management System like WordPress, Drupal or many others, it's entirely likely that there is an SEO plugin that will make implementing canonical tags for all your URLs very easy.