WordPress.com-registered domains

Check this out: http://en.support.wordpress.com/domain-mapping/domain-management/ It looks like you can just change the name servers/a records/whatever. But if your client is not planning on switching back to WordPress.com, I would suggest you transfer to another registrar. It looks like the Automattic domain manager is pretty full featured, however, so maybe that’s not necessary.

What is files.wordpress.com?

CDN / front-end caching: all scripts and stylesheets are served from our CDN. Images are served from our dedicated *.files.wordpress.com domain. https://vip.wordpress.com/documentation/caching/ That page should answer your question regarding the WordPress.com CDN. cybmeta correctly stated that it is for VIP WordPress members only.