How do I hide this item when creating a theme? Or move it to another place?

It is assigned to the code, but how to display it separately? With respect to you await the the answer. Thanks.

      <!-- ITEM & DETAILS -->
        <div id="post-hooks">
          <?php ItemForm::plugin_post_item(); ?>
        </div>

You cannot move it as it is shown via hook.
You can look for item_form hook in plugin files and disable it.

Disabled temporarily using the style in the plugin.

Why don't you make separate hooks on your plugins?

Because it would need extra theme modifications to make it work.