How to add options in autocomplete contact search options?
You can add easily add predefined fields into the autocomplete results by selecting fields under "Autocomplete Contact Search" under "Settings - Search Preferences". 

Adding the Birth Date will not be as easy. Technically you could add an additional option group value to the option group contact_autocomplete_options, but that will be pretty much experimenting at your own risk since this is supposed to be a reserved option group.