Learn Hardcore Dutch: Tom controleert nog één keer de boeking en betaalt de toeslag. - Tom checks the booking one more time and pays the surcharge.

The accent on één distinguishes the numeral one from the indefinite article een (a/an).
You will also see nog een keer without the accent; it means the same, but with the accent you emphasize that it’s exactly one more time.

Is controleren a separable verb? Why doesn’t it split in Tom controleert?

controleren is an inseparable verb borrowed from French. In Dutch:

Inseparable verbs keep their prefix (in this case con-) attached in main clauses, so you never split them.
That is why we say hij controleert (he checks) and not hij de controleert.

How do you conjugate controleren and betalen for third-person singular?

In the present tense, Dutch verbs normally add -t to the stem for he/she/it. For both verbs:

Remove -en to find the stem:
• controleer (from controleren)
• betaal (from betalen)
Add -t for third-person singular:
• hij controleert
• hij betaalt

Why is the subject omitted in the second clause en betaalt de toeslag?

In Dutch, when two verbs share the same subject and are joined by en, you can drop the repeated subject in the second clause. Here Tom is the subject of both actions, so you simply write en betaalt de toeslag instead of en hij betaalt de toeslag.

What does toeslag mean, and when do you use it?

toeslag means extra fee, surcharge, or supplement. You encounter it:

In travel: baggage toeslag on a plane ticket
In hotels: weekend toeslag
On bills: service toeslag
It’s a de-word; the plural is toeslagen.

Why is it de boeking and not het boeking? How do I know which article to use?

Dutch nouns are either de-words or het-words. Unfortunately there is no foolproof rule, so you usually:

Learn the noun together with its article.
Use a dictionary to check.
Over time you’ll notice patterns (e.g. many -ing nouns are de), but initially practice and exposure are key.

Can I move nog één keer after de boeking? Would Tom controleert de boeking nog één keer be correct?

Yes. Dutch allows some flexibility with adverbials. Both orders are correct:

Tom controleert nog één keer de boeking (neutral, emphasis on repeating)
Tom controleert de boeking nog één keer (emphasis shifts slightly toward the booking itself)
The main clause still follows S–V–O order.

Why must betaalt come right after en? Could it go to the end of its clause?

In a main clause with a coordinating conjunction (en), the finite verb stays in second position:

en (conjunction)
betaalt (finite verb)
de toeslag (object)
Moving betaalt to the end would break the standard SVO (subject–verb–object) pattern for coordinated clauses.