Learn Italian: Il politico a cui faccio l'intervista arriva domani. - The politician I am interviewing arrives tomorrow.

Cui is a relative pronoun (meaning "whom" or "which") that we use after prepositions like a, di, or in. The phrase here is fare un'intervista a (to do an interview to someone). Because of that preposition a, we must say a cui (literally, "to whom"). If the verb didn't require a preposition, we would just use che.

Why does the Italian use faccio l'intervista instead of a single verb for "interviewing"?

You can absolutely use the single verb intervistare! But fare un'intervista (literally, "to make/do the interview") is a very natural and common way to express this in Italian. Notice how changing the verb changes the grammar: if you used intervistare, you wouldn't need a preposition, so the sentence would simply use che: Il politico che intervisto arriva domani.

The English translation says "The politician I am interviewing". Why don't we translate the a cui?

In English, we often completely drop connecting words like "who," "whom," or "that" (e.g., "The politician [whom] I am interviewing"). Italian never allows you to drop these relative pronouns. You must always include them to link the sentence together, which is why a cui is strictly required here.

Why is arriva in the present tense if he arrives domani (tomorrow)?