After digging through calendar help
For status (busy/free) - I found the following information:
If the Calendar account you’re using displays your status for an event, you can change the status at any time and still be available to meet during an event.
By default, Calendar sets your status as free during all-day events and as busy during all other events.
... This would indicate that not all calendar (accounts) are going to display this status.
For private appointments - I found the following information:
If your calendar is administered through a CalDAV or Exchange server (for example, through your workplace), you can make a Calendar event private. Private events can’t be viewed by other users, even if you shared your calendar account with them.
.. This might explain why I don't see the private option.
I'm now wondering if this is also true for the visibility of the busy/free status option?