Learn Spanish (Latin America): Las chicas conversaron en la clase ayer.

It tells us who did the action and when. By dropping the -ar from the regular verb conversar (to chat/converse) and adding -aron, we get the "they" form in the completed past tense (the preterite). It means "they conversed".

Could I use hablaron instead of conversaron here?

Yes, they are very similar! Hablar generally means "to speak" or "to talk," while conversar means "to converse" or "to chat." Using conversaron just emphasizes that the girls were having a back-and-forth conversation rather than just speaking.

Why does the Spanish sentence say en la clase when the English translation is just "in class"?

In English, we often drop the word "the" in common location phrases like "in class" or "at school." Spanish is much more strict about keeping the definite article (el, la, los, las) before nouns, so it literally says "in the class."

Is the word ayer necessary if the verb is already in the past tense?

It is not strictly necessary for the grammar, because conversaron already means they conversed in the past. However, adding ayer (yesterday) gives specific context and is a very common "trigger word" that reminds you to use this completed past tense.