free wordpress.com sites are somewhat automatically SEO'd, as long as you use descriptive, relevant titles, headings and content?
is the site verification the only important tool?
No, Keywords are far more important.
On sites built using WordPress, on a .com domain, not the wordpress.com free domain, do the SEO features provided for the wordpress.com sites also work on the .com sites?
Insofar as I understand what you just said, which is not a sure thing, yes.
Google Analytics can be used for the .com sites, even if built using WordPress, correct?
No. A WordPress.com blog is a WordPress.com blog, whatever its URL, and a custom domain upgrade gets you simply a custom domain.