Learn Farsi: هیچ‌کس دلیل را باور نکرد.

Farsi requires a double negative! When you use negative words like hich-kas (nobody) or hich-chiz (nothing), the verb must also be negative. So literally, this sentence translates to 'Nobody did not believe the reason.'

How is the negative simple past formed for the compound verb in this sentence?

The verb here is the compound verb bāvar kardan (to believe). To make it negative in the simple past, you only add the prefix na- to the helper verb kardan, making its past stem nakard. The non-verb part (bāvar) stays exactly the same.

Which ending is used on nakard for the subject hich-kas?

The word hich-kas (nobody) takes a third-person singular verb, just like 'he', 'she', or 'it'. In the simple past tense, the third-person singular form is just the bare past stem with no extra ending added. That is why we just use nakard.

Why do we need the word rā after dalil?

The word rā marks a specific direct object. Because the sentence is about a specific reason ('the reason') that nobody believed, we must place rā right after dalil to show it is the direct target of the action.