You can easily add a comment box to any part of your site by either adding the JFBCComments module to the page(s) you want it to display. For more flexibility, you can add the {JFBCComments} tag directly into a Virtuemart template file (like the Flypage) to show it automatically on each product.
As for the Comments themselves, they are not stored locally. They are all hosted on Facebook.com. You do have the ability to moderate comments though and hide any 'bad' posts from your users or mark them as spam to help Facebook weed out bad users. Facebook also has a great spam engine which generally prevents spam anyways though.
There is no way for a user to edit their own comments, but they can delete a comment they've made. That's simply a Facebook stipulation. They don't want a full conversation to ensue around a comment just to have it changed later to have a different meaning.
For registration, there are many options. You can choose the automatic registration route, used on this site, to automatically create an account. The username can be selected to be the first 3 letters of the first/last name, like here; the full first.last name; the email address of the user; or the FB User ID (a string of numbers). You can also choose normal registration where the user can set their own username/password at registration. It's up to you on whether you want forms or quick registration.
Once the account is created, the username can be used to login using Joomla or they can login through Facebook when they return.
Hope that explains,
Alex