The widget calendar only highlights the start date of the event. The fullcalendar highlights the event's duration.
Event list shortcodes/widgets can be passed a custom template. The default just shows the start date. (See the documentation on this. For the widget there is a 'template' option which takes the same placeholders.).
Similarly for the single events page, that's just the default template. You're encouraged to copy them into your theme and edit them there. See this page.
Clicking an event on the fullcalendar takes you to the event's page. A recurring event has only one page still. By default a single-occurrence event will tell you the start date, a recurring event will show you the next occurrence date. The page templates are completely customisable, and there are plug-in provided functions that can help too.