Hiszem, hogy az uszoda nyitva van.

Hungarian verbs usually show the subject, so hiszem already means I believe. The subject pronoun én is often left out unless you want extra emphasis or contrast.

• Hiszem = I believe
• Én hiszem = I believe (as opposed to someone else)

So in a neutral sentence, Hiszem is the most natural choice.

Hogy means that and introduces a subordinate clause.

So the structure is:

• Hiszem = I believe
• hogy az uszoda nyitva van = that the swimming pool is open

Just like in English, that can sometimes be omitted in English, but in Hungarian hogy is very commonly used in this kind of sentence.

Az is the definite article, meaning the.

• uszoda = swimming pool
• az uszoda = the swimming pool

Hungarian uses definite articles very often, much like English. Here it refers to a specific pool, so az uszoda is natural.

Also, the article is az rather than a because the next word begins with a vowel:

• a bolt = the shop
• az uszoda = the swimming pool

Hungarian often expresses states like open, closed, turned on, finished, etc. with a special construction:

• nyitva van = is open
• zárva van = is closed

Here, nyitva describes the state, and van is the verb to be.

This is a very common pattern in Hungarian, so it is worth learning as a chunk:

• Az ajtó nyitva van. = The door is open.
• A bolt zárva van. = The shop is closed.

No, not in this sentence.

Hungarian often drops van in present-tense sentences with nouns or adjectives:

• A ház nagy. = The house is big.
• Ő orvos. = He/she is a doctor.

But with forms like nyitva, zárva, készen, etc., van is normally used:

• Az uszoda nyitva van.

So this is not the same as a simple adjective sentence where the present-tense is disappears.

For a learner, it is often easiest to treat nyitva as a fixed state-form meaning open in expressions like nyitva van.

It behaves a bit differently from a basic adjective. That is why it is best learned in whole phrases:

• nyitva van = is open
• zárva van = is closed

So although the English translation uses an adjective, in Hungarian it is better to remember the whole expression rather than trying to match it exactly to English grammar.

This is the neutral, straightforward word order:

1. Hiszem = main verb
2. hogy = introduces the subordinate clause
3. az uszoda = subject of the subordinate clause
4. nyitva van = predicate

Hungarian word order is flexible, but it is not random. It often depends on focus and emphasis. This version sounds neutral and natural.

You could change the order for emphasis in some contexts, but learners should first get comfortable with the neutral order.

Yes, and that is actually very common.

• Hiszem, hogy... = I believe that...
• Azt hiszem, hogy... = I think / I believe that...

Azt hiszem is one of the most frequent ways to say I think in Hungarian. In everyday speech, many speakers would prefer Azt hiszem, hogy az uszoda nyitva van or even Azt hiszem, az uszoda nyitva van.

So your sentence is grammatical, but Azt hiszem... is often more idiomatic in daily conversation.

Both can sometimes translate as I think, but they are not exactly the same.

• hiszem is related to believing
• gondolom is related to thinking/supposing

Very roughly:

• Hiszem can sound more like I believe
• Gondolom can sound more like I think / I suppose

In many situations, Azt hiszem... and Azt gondolom... are both possible, but Azt hiszem... is especially common in everyday speech.

A rough pronunciation guide for English speakers:

• hiszem ≈ HEE-sem
• hogy ≈ hodj or hoj (depending on speech; the gy sound is special in Hungarian)
• az ≈ awz
• uszoda ≈ OO-so-daw
• nyitva ≈ NYEET-vaw
• van ≈ vawn

A few important points:

• s in Hungarian sounds like English sh
• sz sounds like English s
• ny sounds like the ny in Spanish señor or roughly ny in canyon
• stress is always on the first syllable of each word

So the stress pattern is:

• HI-szem
• HOGY
• AZ
• USZ-o-da
• NYIT-va
• VAN

Sometimes yes, especially in speech, but beginners should usually keep it.

So you may hear:

• Hiszem, hogy az uszoda nyitva van.
• Azt hiszem, az uszoda nyitva van.

In everyday Hungarian, omission is more common with phrases like azt hiszem than with plain hiszem. For learning purposes, using hogy is safe and clear.

There are two main places where negation could appear, depending on the meaning.

1. Nem hiszem, hogy az uszoda nyitva van.
   = I do not believe that the swimming pool is open.

2. Hiszem, hogy az uszoda nincs nyitva.
   = I believe that the swimming pool is not open.

In the second version, notice that van becomes nincs in the negative:

• nyitva van = is open
• nincs nyitva = is not open

It is grammatical and natural enough, but in everyday speech people often prefer:

• Azt hiszem, hogy az uszoda nyitva van.
• Azt hiszem, az uszoda nyitva van.

So your sentence is fine, but it can sound a little more direct or literary than the very common conversational phrase Azt hiszem....