Hi Wayne,
Thanks for the interest in our plugins.
I can help answer your questions.
We do not have anything that enables you to show events to members or non members.
It is possible that could be done with a customization or using Private Events that only show to logged in users.
We have our themer’s guide for making customization to the templates if you need something deeper.
https://theeventscalendar.com/knowledgebase/themers-guide/
And our Knowledge Base has a lot of articles that might help:
Home
You can test out many of the customizations the core version of the Events Calendar found for free on WordPress.org: https://wordpress.org/plugins/the-events-calendar/
As for paid events, we have the WooCommerce Ticketing plugins to enable you to sell tickets. It does not have any features to connect it to WooCommerce membership though.
Let me know if you have any follow up questions.
Thanks