Learn German: Guten Morgen, mein Schatz! - Good morning, my darling!

You would change it to mein Schätzchen (my little darling). Notice that the vowel a takes an umlaut (ä) when adding -chen. Even though der Schatz is masculine, das Schätzchen is neuter because all words ending in -chen are neuter. Conveniently, the possessive mein looks the same for both masculine and neuter nominative nouns!

Does Schatz literally mean "darling"?

Literally, der Schatz means "the treasure". It is the most common term of endearment in German, used the same way we use "darling", "honey", or "sweetheart" in English.

Why does it say Guten Morgen with an -en ending instead of just Guter Morgen?

This greeting is actually short for Ich wünsche dir einen guten Morgen (I wish you a good morning). Because the morning is the direct object that you are wishing someone, the masculine noun Morgen and its adjective gut must take the accusative -en ending.

Since Guten Morgen is in the accusative case, why isn't it meinen Schatz?

Because mein Schatz is the person you are talking to, not the thing you are wishing them. Whenever you directly address someone in German, you always use the nominative case, so it stays mein Schatz.