Learn Dutch: Ik ben boos omdat het bonken nooit stopt. - I am angry because the banging never stops.

When you use a full infinitive verb as a noun to describe an ongoing activity (similar to adding -ing in English), it always becomes a neuter noun. That means it must always take the article het.

Is bonken the standard noun for a bang, or is this the verb being used as a noun?

It is the verb bonken (to bang or pound) acting as a noun to mean the continuous activity of banging. If you wanted to talk about a single, specific bang, you would use the regular noun de bonk. Using het bonken emphasizes the ongoing action.

Why is the verb stopt placed at the very end of the sentence?

The word omdat (because) introduces a subordinate clause. In Dutch, subordinate clauses push the conjugated verb to the end of the clause. Since stopt is the only verb in that part of the sentence, it goes last.

How would the sentence change if I wanted to say the banging doesn't stop, instead of never stops?

You would simply replace nooit (never) with niet (not), making it: omdat het bonken niet stopt. The word order stays exactly the same because both are adverbs modifying the verb at the end of the subordinate clause.