Has the Block Cache Settings from Drupal 8 been back-ported to Drupal 7? I noticed in Drupal 8 there are options to cache a block:



I was wondering if these options exist in Drupal 7 with a module? Has the feature been back ported? or was it a contrib module to begin with?
No, it's impossible to backport. See https://api.drupal.org/api/drupal/modules%21block%21block.api.php/function/hook_block_info/7's DRUPAL_CACHE_CUSTOM and https://www.drupal.org/developing/api/8/cache/contexts.