Learn Spanish (Latin America): El primo de la niña está en la sala.

Spanish doesn't have an apostrophe "s" to show possession. Instead, you always use the formula "the [thing or person] of the [owner]". Here, el primo de la niña literally translates to "the cousin of the girl".

Why is it de la niña instead of just de niña?

Because "girl" is a common noun, you need to include the word for "the" (la) to say "of the girl". If the owner were a specific name, like Maria, you would drop the "the" and just say el primo de Maria.

Can I change the word order and say la niña de primo to mean the same thing?

No, the word order with de is strict. The person or thing being "owned" (el primo) must always come first, followed by de, and then the owner (la niña).

Why do we use está here instead of es if a cousin is a permanent family member?

Even though being a cousin is a permanent relationship, the sentence is talking about where the cousin is located right now (en la sala). In Spanish, you always use the verb estar (which gives us está) to talk about physical location, no matter who or what is located there.