Learn Dutch: Door het zinken begon de lading snel te roesten. - Due to the sinking, the cargo started to rust quickly.

In this sentence, the infinitive zinken (to sink) is acting as a noun, meaning the sinking. In Dutch, you can turn any infinitive into a noun by simply placing the neuter definite article het in front of it.

Since this lesson focuses on komen te, could we say kwam te roesten instead of begon te roesten here?

They mean different things. Komen te expresses a resulting state, meaning to end up in a certain situation. Beginnen te (used here in the past tense as begon te) marks the start of an action. While kwam te roesten would mean the cargo ended up rusting, begon te roesten is much more natural to describe the onset of this physical process.

Why is the verb phrase begon te roesten split up across the sentence?

Because the prepositional phrase Door het zinken occupies the first position in the sentence. This triggers inversion, placing the conjugated verb begon in the second position and the subject de lading right after it. As usual in Dutch main clauses, the remaining verb parts like te roesten are sent to the very end.

Could we use vanwege or wegens instead of door here?