Contextual filter for related content

Have you tried using the ::listUsage() method of the service this module provides?

To achieve the first scenario I believe something similar to the following code should do the trick:

/**
 * Implements hook_ENTITY_TYPE_view().
 */
function MY_MODULE_node_view(array &$build, \Drupal\Core\Entity\EntityInterface $entity, \Drupal\Core\Entity\Display\EntityViewDisplayInterface $display, $view_mode) {
  /** @var \Drupal\entity_usage\EntityUsage $usage_service */
  $usage_service = \Drupal::service('entity_usage.usage');
  $usage = $usage_service->listUsage($entity);
  if (!empty($usage['node'])) {
    foreach ($usage['node'] as $nid => $qty) {
      $node = Node::load($nid);
      if ($node) {
        $build['extra_link_' . $nid] = $node->toLink(t('The parent node of the node you are viewing is: !title', ['!title' => $node->getTitle()]))->toRenderable();
      }
    }
  }
}

For the second scenario, this module does not provide an API function to retrieve that info directly, but the structure of the information in the database is not complex, you should be able to perform a custom query on {entity_usage} and fetch all "siblings" of the node you are viewing.

Closing for now, feel free to re-open if you need further information.

I needed similar functionality to what is being discussed here.

Some of my sources were Paragraphs so I needed to use listSources() which returned the source_type.

<?php

/**
 * Add Usage output to the template to facilitate "Appears in".
 *
 * Implements hook_ENTITY_TYPE_view().
 */
function iisd_frontend_node_view(array &$build, \Drupal\Core\Entity\EntityInterface $entity, \Drupal\Core\Entity\Display\EntityViewDisplayInterface $display, $view_mode) {
  if ($build['#view_mode'] === 'full') {
    /** @var \Drupal\entity_usage\EntityUsage $usage_service */
    $usage_service = \Drupal::service('entity_usage.usage');

    if ($usage_service instanceof EntityUsage) {
      $sources = $usage_service->listSources($entity, FALSE);

      if (!empty($sources)) {
        $nids = [];
        $render_arrays = [];

        foreach ($sources as $source) {
          if ($source['source_type'] === 'node') {
            $node = Node::load($source['source_id']);

            if ($node instanceof Node) {
              $nid = $node->id();

              if (!in_array($nid, $nids)) {
                $nids[] = $nid;

                $view_builder = \Drupal::entityTypeManager()->getViewBuilder('node');

                $render_arrays[] = $view_builder->view($node, 'teaser');
              }
            }
          }

          if ($source['source_type'] === 'paragraph') {
            $paragraph_entity = Paragraph::load($source['source_id']);
            $parent_node = $paragraph_entity->getParentEntity();

            // If you have nested paragraphs you will need to loop
            // the parent.
            // while ($source->getParentEntity() && $source->getParentEntity() != NodeInterface) {
            //
            // }

            if ($parent_node instanceof Node) {
              $nid = $parent_node->id();

              if (!in_array($nid, $nids)) {
                $nids[] = $nid;

                $view_builder = \Drupal::entityTypeManager()->getViewBuilder('node');

                $render_arrays[] = $view_builder->view($parent_node, 'teaser');
              }
            }
          }
        }
      }
    }

    if (!empty($render_arrays)) {
      $build['appears_in'] = $render_arrays;
    }
  }
}
?>