Based off the screenshots you've two CB plugins or a Joomla system plugin that is loading Facebook API. Please PM backend login credentials and will take a look.
All our tests including numerous users are having no issues with FBC. When an isolated issue on your specific site occurs it typically is not due to the plugin, but a conflict which WILL happen if multiple APIs are loaded.
Please understand you purchased an individual plugin, which does NOT include support. If you are new to such plugins then it's recommend to purchase them with an Advanced subscription so you're more likely to receive timely support.
Additionally incubator project CB Connect offers Facebook login capability without the conflicts as it does not need Facebooks PHP library. This usage is not possible in FBC, which will result in conflicts with other extensions using Facebook API. I've made a note to extend no conflict even further to go as far as renaming classes for next release.