Xristos,
JFBConnect has a profile plugin which works with Virtuemart 1.1.x and 2.x. With that plugin, you can import a user's Facebook profile into Virtuemart.
Beyond that, JFBConnect creates standard Joomla users which can go through the checkout process just like any other user. Our {JFBCLike}, {JFBCComments}, etc tags can also be easily added to Virtuemart to add the Facebook social buttons wherever you want them.
Hope that helps, but if you have other questions, just let us know!
Thanks,
Alex