You handle getting a random post by using the orderby element in a find() or in a Shortcode. If you set the orderby element to RAND() it will put the items in a random order, so then if you set the limit to 1, it will only show one random item, or post.
Other Helpful Documentation on Tips & Techniques
Grouping Admin Menu Items for Post Types
This is very easy with post types generated by Pods. If you create a Custom Post Type with Pods, you can add this to Parent Menu ID: “edit.php?post_type=top_level_post_type” Referenced from this article on stackexchange