I’m glad you like it so far.
When the shortcut picks an event, going back to the calendar doesn't show the day but the week because I'm on week view by default. Is there a way to add in the shortcut to force Calendar to switch to day view systematically?
I had looked into it before posting the shortcut and I could not find an action that would change the Calendar view to “Day”. You would need to change it manually which, I admit, is not very convenient.
Is there a way to only pick All Day events? I typically journal my past activities as All Day events to differentiate them from future, scheduled meetings which are assigned to a particular time.
I modified the shortcut to filter only All Day events.
Is there a way to exclude some calendars? I experienced that even if I hide a calendar A in my app, the shortcut will unhide this calendar A if it happens to pick an event from this calendar A
I modified the shortcut to exclude 2 calendars. In this example, the “US Holidays” and “Birthdays” calendars are excluded. Choose your own appropriate calendars to exclude. You can use the “+” icon in the filter to add more calendars to exclude.
would there be a way to pick a random day, fetch all "All Day" events from that day, copy them as text (both the title and the description), display them in a text reader that shows on my screen as a popup and that just vanishes when I dismiss the popup?
I modified the shortcut to display a popup alert instead of opening Calendar.
I see how to use personal automation but how do you make it run every 3 days? I don't see that option.
I don’t think you can create a personal automation that runs every 3 days. The closest solution would be a weekly automation that runs only 2 days of the week like so:

Here is the link to the updated shortcut: Get Random Calendar Event.
EDIT: I’d like you to be aware that the shortcut would freeze occasionally during testing, especially after running it a couple of times. I’m not sure why. I was able to unfreeze it by quitting the Shortcuts and Calendar applications and waiting a few minutes. I don’t know whether this will be an issue with a personal automation but you should keep an eye on it.