Learn Dutch: Er heerst stilte en ik hoor jouw adem helemaal niet. - Silence prevails and I do not hear your breath at all.

In Dutch, the negation word niet (and the amplified helemaal niet) usually comes after a specific direct object. Here, the specific direct object is jouw adem (your breath), so helemaal niet is pushed to the end of the clause.

What does heerst mean here, and why use er with it?

The verb heersen literally means 'to rule' or 'to prevail'. Dutch frequently uses the combination er heerst to describe a prevailing atmosphere or condition (like 'there is a tense atmosphere' or 'silence prevails'). We use the dummy subject er because the true subject, stilte (silence), is an indefinite noun without 'de' or 'het' in front of it.

Could I say je adem instead of jouw adem?

Yes, je adem is perfectly fine and actually more common in everyday speech. Using the stressed pronoun jouw places a deliberate focus on the fact that it is your breath, fitting the slightly poetic or dramatic tone of this sentence.

Is adem related to the verb for breathing?

Exactly. De adem is the noun for 'breath', and ademen is the verb 'to breathe'. You might also see the word ademhalen (literally 'to fetch breath'), which is another very common verb for breathing.