Learn Farsi: می‌خوام چنین شایعه‌ی مضحکی رو بشنوم!

Demonstrative adjectives of kind, like chenin (such), come directly before the noun they modify without using an Ezafe. You just say chenin shâye'e (such a rumor), not chenin-e shâye'e.

Why is there an -i at the end of the adjective mozhak instead of on the noun?

When using chenin to mean "such a", the indefinite -i suffix attaches to the very end of the noun phrase. Since the adjective mozhak modifies shâye'e with an Ezafe, the -i goes at the end of that entire block: chenin [shâye'e-ye mozhak]-i.

We usually use ro for definite objects. Why is it used here when the phrase has the indefinite -i?

While the -i marks it as "a" rumor, chenin singles out a specific category ("this kind" of rumor). Because the speaker is referring to a very specific type of rumor in their mind, it feels definite enough in context to require the direct object marker ro.

Why is the second verb beshnavam instead of the indicative mishenavam?

The first verb mi-khâm (I want) triggers the subjunctive mood for the second verb because it expresses a desire rather than a stated fact. Therefore, we use the subjunctive prefix be- attached to the present stem of shenidan (to hear).