Facebook – WP integration issue

Hi
I’ve installed FB social plugin and as for its plugin functions my settings work (I’ve sent test posts to both my Timeline and Page and embroidered my site with a range of accessible functions this plugin offers). I’m a bit cautious with widgets wondering if floating visibility (you know what I mean :)) will show faces of my followers and I suspect that this can done only by a widget.
The widget version of like box seems to working but the widget like button set for a Timeline is probably a mistake as it probably serves only the Page, similarly in Recommendation box and recent activity (activity feed?) they should be set for the Page I guess. Anyway, they tend to be in a logged out mode and when I log in and then refresh the site they are logged out again…. Why ?
I haven’t finished with my Open Graph setting – I don’t know how to perform test actions – anytime I submit such I’m given info that I should perform at least one action before their approval. I’ve included the app’s description, URLs, a series of icons etc but haven’t submitted the app’s page yet.