Learn French: Elle a raison, pourtant personne ne l'écoute. - She is right, yet nobody listens to her.

In French, you don't "be" right, you "have" right. The expression is avoir raison (literally "to have reason"). The opposite is avoir tort (to be wrong).

This lesson is about alors and donc (so/therefore). Why is pourtant used here instead?

Alors and donc show consequence (cause and effect). Pourtant means "yet" or "however" and shows opposition instead. If we used donc here (Elle a raison, donc personne ne l'écoute), it would mean nobody listens to her because she is right! Pourtant shows that the second part is surprising or contrasts with the first part.

I'm used to seeing ne ... personne (nobody) around a verb. Why is it personne ne here?

When "nobody" is the subject doing the action, it moves to the front of the sentence. The pattern becomes Personne ne followed by the verb. Since nobody is the one doing the listening here, we say personne ne l'écoute.

What does the l' in l'écoute mean, and why does it go before the verb?

The l' is the direct object pronoun la (meaning "her"), which drops its "a" because écoute starts with a vowel sound. In French, object pronouns usually go right before the verb they belong to, rather than after the verb like they do in English.