The read_page_mailboxes permission is required to be able to respond to messages for a Facebook Page. Currently Facebook has not granted the Bot Libre app this permission, so this functionality only works from our own Facebook pages right now.
We are still hopeful that Facebook may grant us this permission, but they seem to be very restrictive on their API usage.
We do not support posting to groups. Looking into theit API, it seems it is possible, but only for app/game type groups, or groups that you are an admin of and have the additional user_managed_groups permission for. I will look into it.