Learn Dutch: Haar zus is niet getrouwd. - Her sister is not married.

In this sentence, haar is a possessive adjective meaning "her" (belonging to her). But watch out: haar can also be the object pronoun "her" (like in "I see her") and it is also the Dutch noun for "hair"! You can easily tell from the context here that it is the possessive "her" because it is placed right before the noun zus.

Why does niet come right before getrouwd here?

When you use niet (not) to negate a specific adjective, it usually goes directly in front of that adjective. Here, getrouwd acts as an adjective describing her sister, so niet belongs right before it to say she is "not married".

Is getrouwd a verb or an adjective here?

It is originally a past tense verb form from trouwen (to marry), but in sentences like this, it acts exactly like an adjective. In English, you do the exact same thing when you describe someone as being "married".

What is the difference between zus and zuster?

Zus is the standard, everyday word for a female sibling. You might also see the word zuster, but that is older and much more formal. Today, zuster is mostly used to mean a female nurse or a nun. When talking about family members, almost everyone just says zus.