Learn Dutch: De Verenigde Staten zijn heel groot. - The United States is very big.

In English, we usually treat "The United States" as a single entity and use a singular verb ("is"). In Dutch, however, country names that are grammatically plural (like de Verenigde Staten or de Filipijnen) strictly follow their plural form and take a plural verb.

Is the article de mandatory here?

Yes. Most country names in Dutch do not take an article (like Nederland or Duitsland), but geographical names that are plural always require the definite article de.

Since Verenigde Staten is plural, why doesn't groot get an -e ending?

Adjectives only take an -e ending when they are placed directly in front of the noun they modify. Because groot comes after the verb to describe the subject (acting as a predicate adjective), it never gets an extra -e.

Can I use erg instead of heel to mean "very" in this sentence?

Yes, erg groot is also completely correct. Heel and erg are largely interchangeable as adverbs meaning "very". Heel is slightly more typical for literal, measurable traits like size, while erg is often used for subjective qualities, but both are fine here.