Learn Farsi: این ما بودیم که غرب و جنوب را فتح کردیم. - It was us who conquered the west and the south.

In Farsi cleft sentences that emphasize a pronoun, the "to be" verb must agree with that pronoun. Since the pronoun is mā (we), the verb must be the first-person plural budim (we were), rather than a fixed "it was". Farsi also uses in (this) to introduce the emphasized phrase.

So both verbs in the sentence have to match the pronoun mā?

Exactly! In English, we say "It was us who conquered." In Farsi, both the introductory "to be" verb (budim) and the action verb in the second clause (fath kardim) take the first-person plural ending because mā is the subject of both parts.

Why is the direct object marker rā only placed after jonub (south) and not also after gharb (west)?

When multiple specific direct objects are grouped together with va (and), you only need to place rā once at the very end of the list. Here, gharb va jonub (the west and the south) acts as a single block receiving the action, so rā is attached only to the final word.

Why use ke for "who" instead of ki?

ki is strictly a question word used to ask "who?". Whenever you need a relative pronoun to link parts of a sentence together (translating to "who", "whom", "that", or "which" in English), Farsi always uses the universal connector , even when referring to people.