"Hoşça kalın baykuşlar!"

This is adorable

What's wrong with "Bye bye, owls"?

Is there a particle or a case used in Turkish when you are addressing someone in speech, something doing the same thing as "O" in English (eg, "O Mankind) or "ya" and "ya ayuha" in Arabic (eg, "ya akhi" meaning, "O my brother!).

What is the "in" doing in hoşça Kalin ?

"ın" is added to that to first, address more than one person. Second, sound more formal even if only a solitary person is addressed.