Users cannot change their password at account managment

That's how Joomla/Virtuemart work, depending on your configuration. If a user is initially created/registered without a password, they won't ever be shown a password field when they edit their profile. Joomla doesn't show it because it thinks the user doesn't use the standard Joomla authentication.. which it doesn't, since you're user is logging in through Facebook.

To fix, you can change the setting in JFBConnect for "Generate Random Password:" to "Yes". That will let the user log with Facebook and will create them a Joomla password that they can use to log in later with. They'll also be able to edit that password later.

I hope that helps explain,
Alex

JFBConnect doesn't alter the normal registration process through Joomla in any way. If your users are registering through Joomla/Virtuemart directly and not through JFBConnect at all, then if the password is missing, I don't think that would be caused by JFBConnect.

To test, can you try disabling the JFBCSystem, JFBCUser, and JFBCAuthentication plugins. That will completely disable JFBConnect. Then, try registering again. If the password isn't shown, then that means something else is preventing it from showing.

If it works then, let us know. Again though, there's no reason that JFBConnect should be altering 'normal' Joomla users. Our extension simply wasn't designed that way.

Thanks,
Alex

I just tried to register on your site and I couldn't see the password field in Virtuemart like you mention. However, if I go to the Joomla user profile area using the link below, I can see the password fields:
index.php?option=com_user&view=user&layout=form

I'm not sure what's happening in Virtuemart, but I think it's a configuration setting in there that you're having issues with. We don't alter standard Joomla or Virtuemart users that register normally. Is there a reason you think that JFBConnect caused this? If you disable the JFBCSystem, JFBC User and JFBC Authentication plugins and try to register, does the issue still occur? If so, it's definitely not caused by JFBConnect.

I hope that helps you investigate further,
Alex