Learn Dutch: We kijken ademloos terwijl de helikopter aankomt. - We watch breathlessly while the helicopter arrives.

It functions as an adverb here, describing how we watch (kijken). It is formed from the noun adem (breath) and the suffix -loos (less/without). Remember that in Dutch, you don't add an extra ending like the English "-ly" to turn an adjective into an adverb; the base form does both jobs perfectly.

Is ademloos used figuratively or literally in Dutch?

It can be used both ways, exactly like "breathless" in English! You can use it literally if you are out of breath from running, or figuratively, as in this sentence, to mean you are captivated, in suspense, or watching with breathless anticipation.

Why is the verb aankomt pushed to the very end of the sentence?

The conjunction terwijl (while) introduces a dependent (subordinate) clause. In Dutch, dependent clauses force the conjugated verb all the way to the end of that clause.

Aankomen (to arrive) is a separable verb. Why aren't its parts separated here?

Because it is inside a dependent clause! In a standard main clause, the verb splits and the prefix goes to the end (for example: De helikopter komt aan). But when a dependent clause kicks the verb to the end of the sentence, the prefix (aan) and the core verb (komt) crash back together into the single word aankomt.