"Wie loopt er door het park?"
Translation:Who is walking through the park?
What is the rule for when 'er' is and is not included in the English version?
You only translate er as "there" in phrases like er is, er zijn = "there is, there are" - phrases comparable to French il y a or German es gibt.
Dutch er is very versatile, though. We use it in nearly every sentence, and if the sentence makes sense without it, you can generally be safe to leave it out in your English translation.
The English sentence "Who is there walking through the park?" would be rendered as wie loopt daar door het park?, or even as wie loopt er daar door het park? You see that the demonstrative daar is used. So in short, don't see "there" as a translation of er, but of both daar and er .