Learn Hardcore Dutch: De ober zet het warme bord op tafel en controleert onze bestelling. - The waiter places the warm plate on the table and checks our order.

In Dutch every noun is either “common gender” (using de) or “neuter gender” (using het). There are no strict rules that always tell you which is which—you need to learn them along with each noun.
• de ober, de tafel, de bestelling = common gender → de
• het bord = neuter gender → het

Why is it het warme bord and not het warm bord?

Because when an adjective comes before a noun with a definite article (de/het), it almost always takes an -e ending. That’s called adjective inflection:
• het + warm + bord → het warme bord
If there were no article—een warm bord—the adjective stays in its base form after een for neuter nouns.

In zet het warme bord op tafel, why is there no de before tafel?

op tafel is a common way to say “on the table” in a restaurant context, treating tafel generically. You could also say op de tafel if you want to emphasize that specific table, but Dutch often drops the article in set phrases describing where something goes.

Is op tafel zetten a separable verb like opzetten, or is it just zetten + preposition?

Here it’s simply the verb zetten (“to place/set [upright]”) followed by the preposition op indicating location.
• zet + op tafel = “places on the table”
opzetten (separable verb) is a different verb meaning “to set up,” “to switch on,” etc.

Why isn’t the waiter’s name or de ober repeated before controleert onze bestelling?

The sentence uses coordination with en (“and”) and omits the repeated subject in the second clause because it’s the same as in the first clause. This is called subject ellipsis:
“De ober zet … en (hij) controleert …” → “De ober zet … en controleert …”

Why do we say onze bestelling and not ons bestelling?

Dutch possessive pronouns agree with the gender of the noun they modify:
• bestelling is a de-word (common gender) → use onze
• If it were a neuter noun (het-word), you’d use ons

Why does controleert (the verb) come right after en instead of after the subject?

In Dutch main clauses (and in coordinate clauses after en), the finite verb must occupy the second position (V2 rule). Here the conjunction en counts as position one, so the verb controleert comes next, then the (omitted) subject, then the object onze bestelling.