Die probleem bestaan nog.

Yes. In this sentence, die is the definite article, meaning the.

A useful thing to know is that Afrikaans does not change the for gender the way some languages do. So die is used for singular and plural definite nouns in many cases:

• die probleem = the problem
• die boek = the book
• die probleme = the problems

So die probleem simply means the problem.

No. In Afrikaans, die is usually pronounced more like dee.

So:

• die ≈ dee
• not like English die /dai/

That is a very common beginner mistake, because it looks familiar to an English speaker.

More or less, yes. Probleem is a clear cognate of English problem and has the same basic meaning.

The main difference is spelling:

• English: problem
• Afrikaans: probleem

That long ee is normal in Afrikaans spelling and usually signals a long vowel sound.

Here bestaan means to exist.

So the verb is not the ordinary to be; it is specifically the idea that something exists, continues to exist, or is present as a reality.

For example:

• Die probleem bestaan. = The problem exists.
• Die gevaar bestaan nog. = The danger still exists.

Also, be aware that bestaan can have another meaning in other contexts: to consist.

For example:

• Die span bestaan uit vyf mense. = The team consists of five people.

So without uit, in a sentence like this one, it normally means exist.

Because Afrikaans is not saying the problem is still... with is as the main verb. Instead, the main verb is bestaan = exists.

So the structure is:

• Die probleem = subject
• bestaan = verb
• nog = adverb

Afrikaans often expresses the idea directly with bestaan rather than using is plus another word.

In this sentence, nog means still.

So it tells you that the situation continues.

This is a very important Afrikaans word, but it can mean different things depending on context, such as:

• still
• yet
• another / more

Here, because it follows the verb bestaan, the meaning is clearly still:

• Die probleem bestaan nog. = The problem still exists.

Because that is the normal word order in a simple Afrikaans main clause.

Afrikaans usually follows a subject + verb + rest pattern in straightforward statements:

• Die probleem (subject)
• bestaan (verb)
• nog (adverb)

So nog comes after the conjugated verb.

This is very similar to many English sentences:

• The problem still exists.

English puts still before exists, but Afrikaans often places adverbials after the verb in simple clauses.

It is the present tense.

Afrikaans verbs do not change much for person:

• ek bestaan
• jy bestaan
• hy bestaan
• ons bestaan

So bestaan here is just the present-tense form.

Even though it is present tense, it naturally translates with still:

• exists
• still exists

No, not in the same way.

Afrikaans verbs are much simpler than English verbs in the present tense. The verb usually stays the same regardless of the subject.

For example:

• Ek bestaan
• Jy bestaan
• Die probleem bestaan
• Hulle bestaan

So you do not need a special form like English exists for third-person singular.

Afrikaans normally uses double negation, so a negative version would need nie ... nie.

Examples:

• Die probleem bestaan nie. is not the standard full Afrikaans pattern.
• Standard Afrikaans: Die probleem bestaan nie meer nie. = The problem no longer exists.
• Also possible: Die probleem bestaan nog nie. = The problem does not exist yet.

Notice the two nie elements in standard negation.

Also note the difference:

• nog = still / yet
• nie meer = no longer / not anymore

So if you want the opposite idea of the original sentence, nie meer is often the most natural choice.

Yes, you could, depending on what nuance you want.

• Die probleem bestaan nog. sounds a bit more formal or explicit: the problem still exists
• Die probleem is nog daar. is more idiomatic and conversational: the problem is still there

Both are natural, but bestaan focuses on existence, while is nog daar sounds a little more everyday.

It is neutral.

It is perfectly normal in writing, speech, news reports, academic discussion, and general conversation. It is not slang, and it is not especially stiff either.

So this is a very good sentence pattern to learn and reuse.

Yes, absolutely. This is a very productive pattern in Afrikaans:

• Die gevaar bestaan nog. = The danger still exists.
• Die risiko bestaan nog. = The risk still exists.
• Die moontlikheid bestaan nog. = The possibility still exists.

So once you know this structure, you can use it with many abstract nouns.