Az útlevélkérelem új, és a kormányablak ma nyitva van.

Hungarian has two forms of the definite article:

• a before a consonant sound
• az before a vowel sound

Since útlevélkérelem begins with ú, a vowel, the correct form is az.

Examples:

• a kormányablak
• az útlevélkérelem

This is similar to English a / an.

Hungarian makes compounds very freely, so long words are common.

útlevélkérelem =

• útlevél = passport
• kérelem = application, request

So the whole word means passport application.

This is one word in Hungarian, where English would usually use two words.

In the present tense, Hungarian often leaves out van = is in the 3rd person singular when the predicate is:

• a noun
• an adjective

So:

• Az útlevélkérelem új = The passport application is new

This is normal Hungarian, not an omission or casual speech.

Compare:

• A ház nagy. = The house is big.
• A tanár fáradt. = The teacher is tired.

Because nyitva works differently from a simple adjective like új.

nyitva means in an open state and is part of a common Hungarian pattern:

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

So although English uses a simple adjective here, Hungarian uses a state expression plus van.

That is why:

• Az útlevélkérelem új. but
• A kormányablak nyitva van.

Literally, kormányablak means government window, but that literal translation can be misleading.

In modern Hungarian, Kormányablak is the name of a public government customer service office, a kind of one-stop administrative office where people handle official paperwork.

So in practice it means something like:

• government service center
• government office
• administrative service office

It usually does not refer to an actual physical window.

Because és is joining two clauses here, not just two single words.

The sentence has two parts:

1. Az útlevélkérelem új
2. a kormányablak ma nyitva van

Since both parts are full clauses, Hungarian normally uses a comma before és.

Compare:

• Anna és Péter = no comma, just two nouns
• Anna megérkezett, és Péter elment = comma, two clauses

Hungarian word order is flexible and often reflects emphasis.

In a kormányablak ma nyitva van, ma = today appears in a natural neutral position before the predicate.

This word order suggests something like:

• the government office is open today

Other orders are possible, but they may shift emphasis:

• Ma a kormányablak nyitva van. = emphasis more strongly on today
• A kormányablak nyitva van ma. = possible, but less neutral in many contexts

So the original sentence sounds natural and standard.

No, Hungarian adjectives do not agree the way adjectives do in many European languages.

There is:

• no grammatical gender
• no masculine/feminine adjective form
• no special singular/plural agreement in this predicate use

So új stays új.

Examples:

• A kérelem új. = The application is new.
• A kérelmek újak. = The applications are new.

Notice that in the plural predicate, Hungarian may use the plural adjective form újak, but there is still no gender agreement.

The structure is:

• Az útlevélkérelem = subject
• új = predicate adjective

and

• a kormányablak = subject
• ma = time expression
• nyitva van = predicate

So Hungarian is behaving quite similarly to English at a basic level, even though the verb is is missing in the first clause.

You can think of it as:

• The passport application — new
• and the government office today open is

That is not good English, of course, but it helps show how Hungarian is built.

A few helpful points:

• Hungarian stress is almost always on the first syllable
• long vowels matter: ú, é, á are longer than u, e, a

Rough pronunciation:

• útlevélkérelem ≈ OOT-leh-vayl-KAY-reh-lehm
• kormányablak ≈ KOHR-maany-awb-lawk

A few details:

• ú is a long u
• é is like a long ay
• á is a long open a
• ny sounds like the ny in Spanish señor, or the ny sound in British pronunciation of new for some speakers

The most important thing is to stress the first syllable:

• ÚTlevélkérelem
• KORmányablak

Not very naturally.

Word-for-word, nyitva van is something like:

• openly/opened is or
• is in an open state

But the natural English translation is simply:

• is open

This is a good example of why Hungarian often uses set state expressions that should be learned as units:

• nyitva van = is open
• zárva van = is closed
• el van törve = is broken

So it is best to learn nyitva van as a chunk.

Yes. a is the definite article, so a kormányablak means the government office.

Hungarian uses the definite article very often with specific nouns, including offices, institutions, and things already understood from context.

So this sentence is talking about a specific office, or about the office relevant in the situation.

If it were indefinite, you would expect egy:

• egy kormányablak = a government office

But that would change the meaning.