Dit is de negentiende vraag.

Because dit is being used on its own as a demonstrative pronoun: Dit is ... = This is ...

Compare:

• dit is de negentiende vraag = this is the nineteenth question
• deze vraag = this question

So before a de-word noun, you normally use deze: deze vraag.
But when this stands alone and the noun phrase comes later after is, Dutch normally uses dit.

Dutch main clauses usually follow the verb-second rule. That means the finite verb comes in the second position of the sentence.

Here:

• Dit = first position
• is = second position
• de negentiende vraag = the rest

So Dit is de negentiende vraag is the normal Dutch word order for a statement.

Because vraag is a de-word, so its singular definite article is de.

Also, with ordinal numbers like first, second, nineteenth, you often refer to a specific item in a series, so the definite article is very natural:

• de negentiende vraag = the nineteenth question

If you said een negentiende vraag, that would mean a nineteenth question, which is possible in some contexts but much less likely here.

Because negentiende is an ordinal number that behaves like an adjective when it comes before a noun.

In Dutch, adjectives before a noun usually get an -e ending, especially with de-words like vraag.

So:

• de negentiende vraag

That -e is normal here.
You should think of negentiende as nineteenth used adjectivally.

It comes from negentien = nineteen.

Dutch ordinal numbers are usually made with -de or -ste endings:

• tien → tiende
• achttien → achttiende
• negentien → negentiende

So negentiende simply means nineteenth.

A few very common ordinals are irregular, such as:

• eerste = first
• tweede = second
• derde = third

But negentiende is a regular formation.

Yes, in many contexts you can.

There is a small difference in feel:

• de negentiende vraag = the nineteenth question
• vraag negentien = question nineteen / question number nineteen

So if you are talking about a numbered list, test, or worksheet, vraag negentien is very common.
The sentence you have is a bit fuller and more descriptive.

A rough English-style guide is:

dit iss duh nay-ghuhn-TEEN-duh vraakh

A few notes:

• dit has a short vowel, like dit in a clipped English pronunciation
• de is usually weak, like duh
• the stress in negentiende is on TIEN
• vraag has a long aa sound
• the final sound in vraag is a throaty Dutch g/ch sound, not a hard English g

A more careful breakdown:

• Dit
• is
• de ne-gen-TIEN-de vraag

Dit means this and dat means that.

So:

• Dit is de negentiende vraag = This is the nineteenth question
• Dat is de negentiende vraag = That is the nineteenth question

In practice, dit often points to something closer, more immediate, or just introduced, while dat points to something farther away or less immediate.

So in your sentence, dit is the natural choice if you are identifying something right in front of you, on the page, or in the current discussion.