Hello,
And welcome!
As you have a pro subscription, i recommend you to use the Pro tickets support:
www.joomlic.com/support
There, i give an advanced support, and faster reply
And if you open a private ticket, i can help you too with an admin access, to setup iCagenda as you want it. (but as you wrote, the site is not online yet).
So, as a quick explanation (which is valid for any extension, and Joomla articles as well), about URL routing:
If you have a SEF URL of kind [DOMAIN]/index.php/component/icagenda/[EVENT], that means there's no menu item published that can display the event, and so the default site page is used to display the event details view.
It works the same for articles module of Joomla.
But, in iCagenda modules (calendar and iC Event list, as you've got the Pro version), there's option to change the default behavior.
That means you can select a specific menu item of type "list of events" in the calendar module options, to display all events using this parent menu link.
And an additionnal option allows you to display event only if it meets the filters options (by date, category, access...) of the menu item settings.
So, depending on how you've set up the menu items, there are multiple setting possibilities.
The event does not require an image to work, so it was due to another setting changed somewhere else (menu item and or module options).
When (as a general usecase) you want only one link to list events, and filter to display only upcoming events, a solution to show correctly the past event details view can be to create an hidden menu item of type list of events (if hidden in menu, not visible, but can then be used for details view) and to set it with no filtering or only show past events.
But if you main visible link has as alias something generic such as "events", then you don't need (for a good SEO and URL writing) a second menu item, and then you can force module to always use this menu item in the module options "Link to menu" (which is on "auto" by default).
I hope this gives you a bit more information on how the link system works in iCagenda (and Joomla as well)?
Best regards,
Cyril