Hey Scott,
Thank you for reaching out to us!
To prevent your calendar from being indexed by Search Engines, I would recommend you to use a SEO plugin like Yoast.
Also, to prevent individual events from being indexed, you can add the following code snippet (without the <?php opening tag) near the top of your theme’s functions.php file to add the noindex:
https://gist.github.com/elimn/397b1fc8042bf832e813
Regarding your second question, currently there is no “out of the box” way to make a members-only Calendar, but with a bit of custom coding, you can get pretty close. You will find further information about this in the following article:
https://theeventscalendar.com/knowledgebase/making-members-calendar/
I hope this helps! Let me know if you have any other questions and I’ll be happy to assist!
Best Regards,
Patricia