This depends on what role you designated to the registered users https://wordpress.org/support/article/roles-and-capabilities All WordPress roles and access privileges are provided in a table. For example, the role Subscriber can only send content while Contributors can edit their own content. You can also create your very own roles or opt to use WordPress’s default roles. We’d suggest membership plugins manage your registered users but remember the roles should be set according to your website’s needs.
This can’t be done via MEC, you’ll need to use membership plugins and also uncheck the setting for Guest Users (not logged in) to be able to submit events via the frontend submission form. You can force visitors to login in order to submit their event using this addon.
The user can cancel their booking by clicking on a link present in the confirmation email that was sent to them afterward an email is sent confirming their cancelation. However, you’ll need to do the refund manually from your own end. This addon also provides a specific user window whereby they can cancel their own booking by going to their currently booked events.
You can display their information on the frontend using a shortcode but you’ll need to give them back-end access to edit their information so make sure to assign their user status as the Organizer or Speaker. Now that user can edit their information on the organizer/speaker page.
When creating an event you’ll see a new option under the Booking Section called Limitation for User Tab. Enable Display Booking Section Only for Logged in User to achieve this.
Let me know if you have any other questions in the comment area.