Custom module search ranking not working + ranking admin settings not showing properly
Finally I cracked this frigging case!
As it turns out, there was no way for anyone to be able to answer this question since my given information was incomplete. Although in my defence if I knew that I should've given that info, I would've solved the problem long ago(two days) :-D.

Solving problem #1:

Dead simple! In my case I had commented out the following line inside hook_search_execute():

_node_ranking($query);


this functions adds the rankings to the results.

Solving problem #2:

As for this problem, the influence choosing form doesn't show up automatically. The node module, if active in the Active search modules, lists all the factors for all Search active modules. But for a module to list its own factors, it must implement the hook_search_admin() function like this:

function hook_search_admin() {
  // Output form for defining rank factor weights.
  $form['post_ranking'] = array(
    '#type' =&gt; 'fieldset',
    '#title' =&gt; t('Post ranking'),
  );
  $form['post_ranking']['#theme'] = 'node_search_admin';
  $form['post_ranking']['info'] = array(
    '#markup' =&gt; '&lt;p&gt;&lt;em&gt;' . t('Influence is a numeric multiplier used in ordering search results. A higher number means the corresponding factor has more influence on search results; zero means the factor is ignored. Changing these numbers does not require the search index to be rebuilt. Changes take effect immediately.') . '&lt;/em&gt;&lt;/p&gt;'
  );

  // Note: reversed to reflect that higher number = higher ranking.
  $options = drupal_map_assoc(range(0, 10));
  foreach (knowledge_ranking() as $var =&gt; $values) {
    $form['post_ranking']['factors']['node_rank_' . $var] = array(
      '#title' =&gt; $values['title'],
      '#type' =&gt; 'select',
      '#options' =&gt; $options,
      '#default_value' =&gt; variable_get('node_rank_' . $var, 0),
    );
  }
  return $form;
}