Hey Chuck,
Thanks for reaching out.
The core of your question is what you wrote here: “Is there a way to publicly show the number of calendar events, venues, organizers etc.?”
The short answer is “no”, in the sense that our plugins themselves do not offer any way to do this. And so you’ll unfortunately have to use custom coding here to achieve this display of information.
I say “unfortunately” because we cannot help with custom coding, as elaborated upon here → https://theeventscalendar.com/knowledgebase/what-support-is-provided-for-license-holders/
As a quick tip though, WordPress Core itself (i.e., not our plugins, but WordPress itself) has its own function called <me>wp_count_posts() which does exactly what it sounds liked: it counts the number of posts exist for a specified post type.
So you could probably customize your theme to add this sort of information anywhere you want. Check out this page to learn more about the function and how to use it → https://codex.wordpress.org/Function_Reference/wp_count_posts
I hope this information helps!
George