Hello!
Nice rounded picture in events list !
Today, the submission form is only a submission form, which could be opened for public users as well as registered ones.
In the future, a front-end manager will be created (and available in Pro version) to able access for registered users to a frontend edit of own user events.
Today, if you want to grant access to registered users to their own events, you have to grant access to admin, and manage ACL permissions (both in Joomla and iCagenda) to able this group (create a new one dedicated to edit own iCagenda) to have access only to iCagenda, and part of iCagenda you want (iCagenda is having extra ACL permissions for admin, added to the core Joomla permissions)
Best Regards,
Lyr!C