Can I render a region of my drupal site on a non-drupal site?
You can try Web Widgets module to embed.


  Create dynamic snippets of your Drupal site that users can copy and
  paste to their websites.
  
  
  Supported widget styles: iframe, inline, UWA or Google Gadgets.
  Build a view and make a widget from it.
  Embed any other web site content in a widget with a simple widget API.
  


also look in to Embed widgets module.