Learn Italian: Perché l'ispettore stava arrestando l'uomo? - Why was the inspector arresting the man?

This is the past progressive tense, which is used to talk about an action that was ongoing in the past. You build it by combining the imperfect tense of stare (here, stava meaning "he was") with the gerund form of the main verb (here, arrestando meaning "arresting").

How do we get the -ando ending in arrestando?

The dictionary form of the verb is arrestare (to arrest). To make the "-ing" form (called the gerund) for verbs that end in -are, you drop the -are and add -ando. If the verb ended in -ere or -ire, you would add -endo instead (like leggendo or dormendo).

In English, we swap the words to ask "was the inspector...". Why doesn't Italian do that here?

In Italian, you don't usually need to flip the subject and verb to ask a question. You just keep the normal statement order (l'ispettore stava arrestando) and either put a question word like perché at the front, or simply change your tone of voice to go up at the end of the sentence.

Why do both ispettore and uomo use the article l'?