Learn Farsi: این اتفاق دیروز افتاد. - This incident happened yesterday.

You are right! By itself, oftādan means "to fall". However, when paired with the noun ettefāq (incident/event), it forms the compound verb ettefāq oftādan, which means "to happen" or "to occur". So literally, the sentence says "This incident fell yesterday."

How do I make this sentence negative to say the incident didn't happen?

You add the negative prefix na- to the verb. But because oftād starts with a vowel sound, we insert a "y" sound between them to make it easier to pronounce. So, na- + oftād becomes nayoftād. The negative sentence is: in ettefāq diruz nayoftād.

Why doesn't the verb oftād have a personal ending at the end of it?

In the simple past tense, the third-person singular form (used for "he", "she", or "it") is identical to the bare past stem of the verb. Since the subject here is in ettefāq ("this incident", which acts as an "it"), we just use the stem oftād with no extra endings.

Why is diruz (yesterday) placed right before the verb?

In Farsi, verbs almost always go at the very end of the sentence. Time words like diruz usually go in the middle (or sometimes at the very beginning). The standard word order here is Subject (in ettefāq) + Time (diruz) + Verb (oftād).