When a scheduled deep scan has started I can see the Event history entry that says "Scheduled virus scan has started" but how can I tell when it has completed and how can I view the status and progress of the scan?
I am also only an F-Secure user.
I can see the Event history entry that says "Scheduled virus scan has started"
If your experience is about Windows 10 (at least), then, in addition to the Event list, a toast should appear in the notification area when starting a scheduled scan. With related wording and an ability to skip scheduled scan (actually, during any stage of scanning).
but how can I tell when it has completed
There will be another toast. With some information results and the option to open a scan log report. In addition, the Event list should change its entry about "... has started" to "... has completed" (or so).
and how can I view the status and progress of the scan?
With current design, perhaps, it cannot be done. Let's say is a bit of obscurity. This is partly because the scanning is done in the background and, by design, should not distract the user unnecessarily. All actions (in relation to detected dangerous objects) will be applied automatically (if possible). After completing the scan, you can view the report.
I also think that this is not always optimal. I often want to know how long the scheduled scan will take (or at least at what stage now). It is possible that there are "undocumented" steps to find out this information (for example, using Windows Events journal or whatever). But this is not friendly anyway.
However, I think it is best to schedule these scans during the hours and days when it is expected that you will not need to use the system (and therefore know about anything other than the results).