If you don't mind, can you post the enabled User plugins you have running on your site? That will help us narrow down if one of them is redirecting the user.. usually they're named obviously like.. "Autologin" or "Redirect after Login".
The Facepile can be configured to show friends who have Liked a page or have signed up for your application. The avatar pictures will only be for friends, and not 'everyone'. You can read more about the specifics of the JFBCFriends/Facepile plugin on Facebook's page below:
developers.facebook.com/docs/reference/plugins/facepile/
Specifically, the quote below is probably what you're looking to verify:
The plugin only displays friends photos. If the user does not have friends who have liked your page or have connected to your site, no faces will be shown.
Regarding random photos of registered users, we don't have this ability. Not all registered users may come from Facebook. If you want something like this, we'd recommend looking into Community Builder or JomSocial which are on-site social networking components. JFBConnect is more tailored for integration between Facebook and Joomla, but not for creating a 'mini-Facebook' on your site.
Finally, when a post is made to a user's wall, there's 2 elements - 1 is the message itself, which you set in the JFBConnect Wall Posts configuration area. The 2nd is a description of the page that you're linking to. You can 'describe' the page to Facebook by using the Open Graph tags, which let you set the title, description, preferred image, or a slew of other things to let Facebook know how to represent that page in the wall. If the Open Graph tags aren't set, it will use the standard meta title/description from your page and 'guess' the best image. Additionally, Facebook only scrapes your site every 24-72 hours, so an update to the meta/Open Graph tags may not be shown in a wall post for a few days. You can use the linter to see what Facebook sees about your page:
developers.facebook.com/tools/lint/
You can specify Open Graph tags for your whole site in the Social tab of JFBConnect, and override the tags for specific pages by inserting {JFBCGraph description=my site} and {JFBCGraph title=My Better title}, etc on the page.
Hope this all helps, and good luck!