Learn German: Wir schützen die Umwelt. - We protect the environment.

You spotted it! It's made of um (around) and die Welt (the world). So, die Umwelt literally translates to the "around-world" or the world around us.

Is there a rule to help me remember that Umwelt is feminine?

Yes! In German, compound words always take the gender of their final noun. Since the base word is die Welt (the world), die Umwelt is also a feminine noun.

Why is it die Umwelt here? Is it nominative or accusative?

It is in the accusative case because it is the direct object receiving the action of the verb schützen (to protect). It looks identical to the nominative case because feminine nouns do not change their die article in the accusative.

How would I combine this sentence with a weil (because) clause, like "We protect the environment because it is important"?

You would say: Wir schützen die Umwelt, weil sie wichtig ist. The main sentence stays exactly the same, but we add a comma before weil, and the verb in the second part (ist) gets pushed to the very end. Also, notice that we use sie (she/it) instead of es because Umwelt is a feminine noun!