Hi,
sorry for late reply, we wait to reply because we were looking for a solution.
Facebook login problem
This is a conflict with some JS of your template. You can try at
http://lnx.occupiamoci.org/index.php?option=com_users&view=login&Itemid=255 and works. We will check some possible solution.
Language problem
The date format on form is always Y-m-d because is the required by the script. This not follow the configuration because the date is not rendered by PHP.
For language string this is a issue and we will fix in next release. Thanks for report it. For now if you want italian language you can edit from file /components/com_jsn/assets/js/bootstrap-datepicker.js at line 372.
Tab "persone fisiche" problem
in your template missing some Bootstrap classes. to fix this add this code at the start of file templates/purity_iii/css/themes/occupiamoci/template.css
@import url(../../../../../media/jui/css/icomoon.css);
.input-prepend > *{display:inline-block !important;}
.chzn-container{width:235px !important;}
.chzn-drop{width:233px !important}