Learn German: Falls der Schiedsrichter das Foul nicht pfeift, protestieren wir. - If the referee does not call the foul, we protest.

Both mean if, but falls is strictly conditional (in case), whereas wenn can mean if or whenever/when. Using falls makes it absolutely clear that you are talking about a specific condition or possibility, not a point in time.

What does pfeift mean here? I thought it meant to whistle.

You are right! The verb pfeifen literally means to whistle. In sports contexts, it is commonly used to mean blowing the whistle to referee a game or to call a foul, as the referee is doing here.

The lesson is about zugunsten and zuungunsten. How would I add to this sentence that the referee calls the foul in our favor?

You could say zugunsten von uns or use the fixed phrase zu unseren Gunsten. The sentence would be: Falls der Schiedsrichter das Foul nicht zu unseren Gunsten pfeift, protestieren wir. While zugunsten typically takes the genitive case, personal pronouns often use von plus the dative, or a possessive structure instead.

If we wanted to say we protest to the disadvantage of the other team, how would we use zuungunsten?

You would follow it with the genitive case. For example: ... protestieren wir zuungunsten der anderen Mannschaft. This means your protest is specifically aimed at creating a disadvantage for the opposing team.