Learn Polish: Kochanie, gdzie jesteś? - Darling, where are you?

Yes! Kochanie is a noun formed directly from the verb kochać. In Polish, you can often turn a verb into a noun by adding endings like -nie or -cie. While it literally means the act of loving, it is commonly used as a sweet nickname meaning darling or sweetheart.

When we address someone directly in Polish, we usually change the word ending (the Vocative case). Why doesn't kochanie change here?

You are right that nouns usually change when addressing someone directly. However, kochanie is a neuter noun because it ends in -e. For neuter nouns, the direct address form (Vocative case) is exactly the same as the basic dictionary form.

Since kochanie is a neuter noun, does that mean it doesn't change depending on who I am talking to?

Exactly! The word kochanie is always grammatically neuter, whether you are saying it to a man or a woman. Because of this, if you want to add the word for my, you must always use the neuter form: moje kochanie.

Why isn't the word for you (ty) used before jesteś?

Polish verb endings already tell you exactly who is doing the action. Because jesteś specifically means you are, adding the pronoun ty isn't necessary. You would only include it if you wanted to strongly emphasize the you.