Learn Italian: Che interrogatorio che ci ha fatto la polizia! - What an interrogation the police put us through!

The first che means "what a" (as in "What an interrogation!"). The second che is a pleonastic (meaning redundant) word. It doesn't add any new grammatical meaning, but Italians frequently use it in spoken exclamations to add emotional emphasis to the noun that just came before it. You could drop the second che and the sentence would still be grammatically correct, but less expressive.

Why is the subject, la polizia, placed at the very end of the sentence?

In Italian exclamations and relative clauses, it is very common to invert the word order and put the subject at the end. This is done for better rhythm and emphasis. Saying ...che la polizia ci ha fatto! would sound a bit clunky. Putting the subject at the end keeps the listener's focus firmly on the intense action right after the emphatic che.

Why use the verb fare (ha fatto) to mean "put us through"?

In Italian, the standard collocation for "to interrogate someone" is fare un interrogatorio a qualcuno (literally "to do an interrogation to someone"). While English uses the vivid phrasal verb "put through" to express the ordeal, Italian relies on the highly versatile verb fare.

What role is the pronoun ci playing here?