Learn Croatian: Znate li išta o nestanku? - Do you know anything about the disappearance?

While both can translate to 'anything' or 'something', išta is specifically used in questions, conditions, or negative sentences to mean 'anything at all'. Using nešto would sound more like 'Do you know something about the disappearance?' implying you already suspect that they do.

Why does the word for disappearance, nestanak, become nestanku?

This happens because of a rule called the 'fleeting a'. In masculine nouns like nestanak, the final a often disappears when you add grammatical endings. Since it follows the preposition o (about), it needs the locative ending -u, so nestanak drops the a and becomes nestanku.

What case is išta in this sentence?

It is in the accusative case because it acts as the direct object of the verb znate (you know). For the pronoun išta, the accusative form is exactly the same as its base nominative form.

Could I use ikoji instead of išta in this sentence?

No, because ikoji means 'any' when it acts as an adjective attached to a noun (for example, 'ikoji detalj' meaning 'any detail'). Išta acts as a standalone pronoun meaning 'anything', which is exactly what you need here since you are not modifying another word.