Learn Turkish: Onların yeni sultanı kimmiş? - Who was apparently their new sultan?

Adding the reported past suffix -miş to kim (who) changes "Who is it?" to "Who is it apparently?" or "Who did you hear it was?". You use kimmiş instead of kimdi (who was it) when asking about news, rumors, or information you are learning second-hand.

Why does sultan have an -ı at the end? Doesn't Onların already mean "their"?

Yes, but Turkish requires both parts of the relationship to have a suffix. When you have a possessor like Onların (their), the possessed object must take a possessive suffix. Here, the -ı on sultanı completes the grammatical link for "their sultan".

Since the pronoun is plural (Onların), shouldn't the word be sultanları instead of sultanı?

It can be, but it doesn't have to be! Both Onların yeni sultanı and Onların yeni sultanları are grammatically correct. When the plural pronoun (Onların) is already explicitly stated, Turkish speakers often drop the plural part of the possessive suffix (-ları) and just use the singular one (-ı) to avoid repetition.

Why is the question word (kimmiş) at the very end of the sentence?