I notice that the buyers do not have access to the Calendar and Client Log menus on their client website. Why is that?

From the system settings, the Buyers do not have access to the Calendar and Client Log page. But you can grant them access to this page from the global settings of the product they purchased.

To do that, go to Billing > Products and click edit from the options drop down list to the right of the product they purchased. In the 'Access' tab of the product wizard, scroll down to the 'Content permissions' section > 'Pages' > check the box in front of the Calendar and Client Log pages > click the button 'Save & Exit' at the bottom.

Then you can login as one of the buyers (in Contacts > Buyer Name > link 'Login as {Buyer Name}' in the top right corner of their profile) to check on their private portal if the 'Calendar' and 'My Logs' menus appear on their private client website.