Learn Hardcore Turkish: Mezuniyet törenine davet edildim. - I was invited to the graduation ceremony.

törenine is in the dative case, which corresponds to English “to” or “toward.” In Turkish the dative suffix is -e or -a, chosen by vowel harmony. Since tören has a front, unrounded vowel (ö), you use -e, giving tören + e → törene. The full form törenine just shows the noun stem tören (ending in n) plus -e; you see -ne, but that n is part of tören, not a separate suffix.

Why does törenine look like it has -ne instead of just -e? Where does the extra n come from?

Turkish stems remain intact when you add case endings. The stem is tören (t ö r e n). Adding the dative -e gives törene, which you read as töre n e. It might look like -ne, but it’s simply the stem’s final n plus the suffix e.

How is the word Mezuniyet built?

mezuniyet comes from the Arabic-derived root mezun (“graduate”) plus the nominalizing suffix -iyet, which creates abstract nouns. So:
mezun (“graduate”) + -iyet → mezuniyet (“graduation”).

What is davet etmek, and how do we form its passive?

davet etmek literally means “to do an invitation” – davet is a noun (“invitation”), etmek is the light verb “to do/make.” To make it passive you add the suffix -(i)l to etmek, giving edilmek (“to be invited”). So:
davet etmek (“to invite”) → davet edilmek (“to be invited”).

How do we arrive at davet edildim (“I was invited”)?

Start with the passive infinitive davet edilmek. Then:
1) attach the past tense marker -di → edildi
2) add the 1st person singular agreement -m → edildim
Putting it together: davet edildim = “I was invited.”

Why is this sentence in the passive? How would I say it in the active voice?

The passive shifts focus onto the person being invited (you or “I”), not on who did the inviting. If you want an active version, you must supply an agent and use davet etmek directly:
Beni mezuniyet törenine davet ettiler.
Literally “They invited me to the graduation ceremony.”

Can I add the pronoun ben to say “I was invited”?

No—Turkish passive constructions treat the invited person as the grammatical subject, and the suffix -m already marks “I.” Adding ben would clash with subject–verb roles (and sound odd). You simply say Mezuniyet törenine davet edildim.

Why aren’t there any words for “the” or “a” in this Turkish sentence?

Turkish has no articles. Definiteness or indefiniteness is usually inferred from context or marked by case endings (e.g. accusative for definite direct objects). Here, törenine (“to the ceremony”) is understood as a specific ceremony by context, without a separate word for “the.”