Hi Robert,
with the settings as shown in screenshot of your initial post all registered users are generally able/allowed to create events and venues.
With the Access level "Calendar Partners" you may hide the menu items but this will not forbid creation etc., it's only a "view" permission not influencing "do" permissions.
If you don't want to allow all registered users event/venue creation you need to create a Joomla user group where you add all relevant users. Then on JEM Control Panel click on Options (top right), select this group and set Create and Edit Own to Allowed. After saving go back to JEM Settings User Control and limit Create Events / Create Venues to administrators.
If you want to autiomatically publish new stuff you need to keep Autopublish allowed for all registered users as in your screenshot.
It's a complex matter so I would suggest to create a test site and play around.