What is the name of the table where view modes are stored?
View modes are stored in the configuration entity entity_view_mode which you can load like any other entity:

$view_mode = \Drupal::entityTypeManager()
  -&gt;getStorage('entity_view_mode')
  -&gt;load('node.teaser');


To load all view modes for the entity type node:

$view_modes = \Drupal::entityTypeManager()
  -&gt;getStorage('entity_view_mode')
  -&gt;loadByProperties(['targetEntityType' =&gt; 'node']);


View modes don't store much data other than a label for the view mode name.

How a view mode is displayed for a specific content type is stored in a different entity:

$display = \Drupal::entityTypeManager()
  -&gt;getStorage('entity_view_display')
  -&gt;load('node.article.teaser');


The usage depends on how you define what being used means. If you mean with not used that it is not configured in a content type, which you can query in the config entities mentioned before, this doesn't mean necessarily, that the view mode is not used anywhere. If you configure an entity to be displayed in a view mode, for example in a View or a entity reference field, and this view mode is not configured in the content type, then it fallbacks to the default view mode.