Birthdays
From dmfswiki
Android does not offer a native way for contacts' birthdays to be shown in the calendar - at least not for non-Google accounts.
One possible solution is Birthday Adapter by Dominik Schürmann. It provides a calendar with all contacts' birthdays which can then be displayed in all calendar applications using the standard Android calendar API.
Birthday adapter is open source (GPLv3). It is available from F-Droid (free) or from the Google Play Store (1 €). Source Code is available on GitHub.
Issues
Depending on your device it might be necessary that you use a specific date format when you add a birthday to a contact. These formats can be found on the following page; http://dmfs.org/carddav/?date_format