Learn Farsi: هیچ‌کس چنین حرف مزخرفی را باور نمی‌کند.

The word chenin means such or this kind of. Unlike regular descriptive adjectives that follow a noun and connect with an Ezafe, demonstrative adjectives of kind like chenin and chenân come directly before the noun phrase, and they never take an Ezafe.

Why is there an -i at the end of mozakhrafi?

When using chenin to mean such a, the noun phrase usually takes the indefinite suffix -i. Here, the core noun phrase is harf-e mozakhraf (absurd talk or nonsense). The suffix -i always attaches to the very end of the entire noun phrase, resulting in harf-e mozakhrafi.

Isn't it a contradiction to have both the indefinite -i and the specific object marker râ on the same phrase?

It looks contradictory, but this is a classic Farsi structure you will see often. The -i is required by chenin to build the meaning such a thing. However, in the context of the sentence, such a nonsense refers to a specific statement that was just made. Because it points to a specific direct object receiving the action of the verb, it takes râ.

Why is the verb negative (nemi-konad) if hich-kas already means nobody?

Farsi requires negative concord, often called a double negative in English. Whenever you use a negative pronoun like hich-kas (nobody) or hich-chiz (nothing), the verb must also be conjugated in its negative form. A literal translation would be: Nobody doesn't believe such a nonsense.