Show Facebook Birthdays & Events
Facebook removed functionality to access birthdays & events by means of a calendar subscription. The only option left is to install Facebook app on your iOS device.
Birthdays
To see birthdays originating from Facebook you have to give Facebook access to your Contacts in device Settings.
Facebook then will add birthdays to your contacts (see http://mygooi.com/did-facebook-kill-the-birthday/ for some background info).
If you don't have a mobile number of your contact Facebook doesn't recognize this person as a friend.
Events
So in order to see events originating from Facebook you have to give Facebook access to Calendars in device Settings.
Hide Facebook Birthdays & Events
Birthdays
To hide birthdays originating from Facebook you have to deny Facebook access to Contacts in device Settings.
Device Settings > Facebook > Contacts = Off
Events
In order to hide events originating from Facebook you have to deny Facebook access to Calendars in device Settings.
Device Settings > Facebook > Calendars = Off