How to get the avatar and name

You are right. I didn't notice that.
What about avatars ? Can we feed them into Drupal's user picture ?

For those who are interested.

It seems that FB user picture can't be retrieved through query parameter hence it can't be mapped in the connector (if this is possible, please let me know).

However, you can fetch it with the following code taken from fboauth.module

  // Taken from fboauth.fboauth.inc
  if ($user->uid && variable_get('user_pictures', 0)) {
    $picture_directory =  file_default_scheme() . '://' . variable_get('user_picture_path', 'pictures');
    if(file_prepare_directory($picture_directory, FILE_CREATE_DIRECTORY)){
      $picture_result = drupal_http_request('https://graph.facebook.com/' . $remote_id . '/picture?type=large');
      $picture_path = file_stream_wrapper_uri_normalize($picture_directory . '/picture-' . $user->uid . '-' . REQUEST_TIME . '.jpg');
      $picture_file = file_save_data($picture_result->data, $picture_path, FILE_EXISTS_REPLACE);

      // Check to make sure the picture isn't too large for the site settings.
      $max_dimensions = variable_get('user_picture_dimensions', '85x85');
      file_validate_image_resolution($picture_file, $max_dimensions);

      // Update the user record.
      $picture_file->uid = $user->uid;
      $picture_file = file_save($picture_file);
      file_usage_add($picture_file, 'user', 'user', $user->uid);
      db_update('users')
        ->fields(array(
        'picture' => $picture_file->fid,
        ))
        ->condition('uid', $user->uid)
        ->execute();
    }
  }

Laurent