Learn Italian: Paghi la tassa per il permesso, per favore.

Because this is a formal command addressed to Lei (formal "you"). For verbs ending in -are like pagare, the formal imperative ending is -i. If you were speaking informally to a friend (using tu), you would say paga.

Why is there an "h" in paghi?

The verb is pagare, which has a hard "g" sound (like in "go"). When we change the ending to -i for the formal imperative, adding the "h" keeps that hard "g" sound. Without the "h", pagi would be pronounced with a soft "g" (like in "gem").

The translation says "fee", but doesn't tassa mean "tax"?

It can mean both! In Italian, tassa is often used for specific administrative charges, fees, or duties (like a fee for a permit or a university tuition fee). For general income taxes, Italians usually use the word imposta, though tassa is frequently used as a catch-all term in everyday speech.

Could I say "Paghi Lei la tassa" to be extra polite?

You usually drop the subject pronoun in commands, even formal ones. However, you can include Lei after the verb for emphasis or to clarify who you are speaking to (e.g., Paghi Lei, non lui - You pay, not him). But just Paghi, combined with per favore, is perfectly polite on its own.