Make Facebook comments on Facebook page show up on my Drupal site
You can have a look at this Facebook Comments Social Plugin Module


  Implement Facebook commenting with settings on the level of both
  content type and node. This module comes with a Facebook Comments
  block so you can have comments anywhere on your site.


There are another modules which support your functionalities -> FB Comments Box


  This module gives your site the ability of using Facebook's Comments
  Box social plugin, i.e. comments on your site powered by Facebook. It
  provides an easy way to configure Facebook Comments parameters (like
  theme, administrators, number of posts, node types to attach to) and
  then exposes the generated code as a block for you to insert into a
  region of your choice. This module is intended for anyone who wants to
  put Facebook Comments on their Drupal site in addition to or instead
  of Drupal comments from core.