A nyilvános információ fontos.

Yes. A is the Hungarian definite article, so it corresponds to the.

• a is used before a word that starts with a consonant sound
• az is used before a word that starts with a vowel sound

Here the next word is nyilvános, which starts with ny, a consonant sound, so we use a:

• a nyilvános információ = the public information

Hungarian often uses the definite article in places where English might also say just public information, so the most natural translation depends on context.

Because the article agrees with the next word immediately after it, not with a later word.

Here the article is directly before nyilvános:

• a nyilvános információ

Since nyilvános begins with ny (a consonant sound), the correct article is a.

Compare:

• a nyilvános információ
• az információ

So the adjective between the article and the noun affects which article you use.

Because in Hungarian, adjectives normally come before the noun, just as they do in English.

So:

• nyilvános információ = public information
• fontos információ = important information

This part is quite straightforward for English speakers.

Also, Hungarian adjectives usually do not change form to agree with the noun in number, gender, or case in simple noun phrases like this.

In Hungarian, the verb van (to be) is usually left out in the present tense, third person when the predicate is a noun or adjective.

So:

• A nyilvános információ fontos. literally: The public information important. natural English: The public information is important.

This omission happens in sentences like:

• A ház nagy. = The house is big.
• Péter orvos. = Péter is a doctor.

But the verb appears in other persons:

• Én fáradt vagyok. = I am tired.
• Te fáradt vagy. = You are tired.

And also often in past/future or certain emphasis patterns.

Because fontos is the predicate adjective here: it tells us what the subject is like.

A very neutral Hungarian sentence pattern is:

• [subject] + [predicate]

So:

• A nyilvános információ = the subject
• fontos = important / the predicate

That gives the neutral statement:

• A nyilvános információ fontos.

Hungarian word order is flexible, but changes in order often affect emphasis rather than basic meaning.

Not here. In this sentence, nyilvános stays the same.

Hungarian does not have grammatical gender, so adjectives do not change for masculine/feminine/neuter like they do in some other European languages.

In a simple singular noun phrase:

• nyilvános információ = public information
• fontos információ = important information

If the noun becomes plural, the adjective still usually stays unchanged in attributive position:

• nyilvános információk = public pieces of information / public information items

So this is easier than in many Indo-European languages.

The version with a is definite:

• A nyilvános információ fontos. = The public information is important / Public information is important, depending on context.

Without the article:

• Nyilvános információ fontos.

this sounds more general, headline-like, or less natural in many ordinary contexts. Hungarian often prefers an article where English might omit one.

So for a normal full sentence, A nyilvános információ fontos is the safer, more standard form.

A rough pronunciation guide:

• a = short aw / o-like sound
• ny = like the ny in Spanish señor or the ni in onion
• í and á, ó are long vowels
• c in információ is pronounced ts
• Hungarian stress is usually on the first syllable of each word

Very rough approximation:

• a nyilvános információ fontos
• aw NYEEL-vaa-nosh IN-for-MAA-tsee-oh FON-tosh

This is only approximate, but a few key points matter a lot:

• ny is a single consonant sound
• vowel length matters: a vs á, i vs í, o vs ó

In Hungarian, accent marks are not optional decoration. They are part of the spelling and usually show a different vowel quality and/or vowel length.

For example:

• a and á are different vowels
• o and ó are different
• i and í are different

So in:

• nyilvános
• információ

the accented vowels must be learned as part of the word.

This matters because changing vowel length or quality can change the word or make it sound incorrect.

If both the subject and the predicate are plural, you would usually say:

• A nyilvános információk fontosak. = The public information items are important.

Changes:

• információ → információk (-k marks plural)
• fontos → fontosak (predicate adjective agrees in number here)

So singular:

• A nyilvános információ fontos.

Plural:

• A nyilvános információk fontosak.

Add nem before the predicate:

• A nyilvános információ nem fontos. = The public information is not important.

This is the normal way to negate this kind of sentence.

Pattern:

• X fontos. = X is important.
• X nem fontos. = X is not important.

Yes, információ is a normal Hungarian word and is very common, especially in formal, official, academic, or general contexts.

It is a loanword, and it looks similar to English information, which makes it easy to recognize.

Depending on context, Hungarian might also use other words, such as:

• adat = data, piece of information
• tájékoztatás = information, briefing, informing
• hír = news

But in your sentence, információ is perfectly natural.