Az igazolványkép új.

Here, az is the definite article, so it means the.

Hungarian has two forms of the definite article:

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

Because igazolványkép starts with i, Hungarian uses az: Az igazolványkép.

In this sentence, az does not mean that.

Hungarian changes the form of the definite article depending on the sound that follows it.

• a ház = the house
• az alma = the apple

Since igazolványkép begins with a vowel sound, the correct form is az igazolványkép.

Yes. It is a single compound noun.

It is made from:

• igazolvány = ID card / document / identification
• kép = picture / image / photo

So igazolványkép means ID photo or passport-style photo, depending on context.

Hungarian often builds meanings by combining nouns into one word.

In Hungarian, the verb to be is often omitted in the present tense, third person, when the predicate is a noun or an adjective.

So:

• Az igazolványkép új. = The ID photo is new.

Literally, Hungarian says something like The ID photo new.

But in other persons, the verb appears:

• Új vagyok. = I am new.
• Új vagy. = You are new.

And in past or future, it also appears:

• Az igazolványkép új volt. = The ID photo was new.

Good question. Hungarian adjectives do usually come before the noun when they directly describe it:

• az új igazolványkép = the new ID photo

But in Az igazolványkép új, új is not just modifying the noun inside the noun phrase. It is the predicate of the sentence. In English, this is the difference between:

• the new ID photo
  and
• the ID photo is new

So:

• az új igazolványkép = the new ID photo
• az igazolványkép új = the ID photo is new

Új means new.

In this sentence, it describes the state or quality of the photo: the photo is new, not old or not the previous one.

It can also be used before nouns:

• új könyv = a new book
• új igazolványkép = a new ID photo

It is in the nominative form, with no special ending.

This is the basic dictionary form of the noun, used here as the subject of the sentence.

So:

• az igazolványkép = the ID photo

There is no object marking or other case suffix here.

Yes, Hungarian word order is flexible, but changing it usually changes the focus or emphasis.

The neutral sentence is:

• Az igazolványkép új. = The ID photo is new.

You might also hear:

• Új az igazolványkép.

This can sound more contrastive or focused, as if stressing new.

So the original sentence is the most straightforward, neutral way to say it.

A rough pronunciation is:

• az ≈ awz
• igazolványkép ≈ ee-gaw-zol-vaany-kayp
• új ≈ something like oo-y

A few useful notes:

• gy in Hungarian is a special consonant, somewhat like the d in British duke or the dy sound in module for some speakers.
• á is a long vowel.
• é is pronounced like ay in say, but pure and longer.
• új contains a long ú.

The stress in Hungarian normally falls on the first syllable of each word:

• Igazolványkép
• Új

Yes, az can also mean that, but not in this sentence.

Here is how you can tell:

• When az comes directly before a noun like an article, it usually means the.
• When it is used as a demonstrative, it often has a different structure, such as:
  • az a kép = that picture

So in Az igazolványkép új, az is simply the definite article the.

Yes, very possibly.

Igazolványkép and igazolványfotó can both refer to an ID photo. Which one sounds more natural may depend on region, context, or personal preference.

• kép = picture/image
• fotó = photo

So both can be understandable, but igazolványkép is a perfectly normal Hungarian form.

Yes.

Singular:

• Az igazolványkép új. = The ID photo is new.

Plural:

• Az igazolványképek újak. = The ID photos are new.

Notice two things:

• igazolványkép becomes igazolványképek in the plural
• új becomes újak when it is a predicate with a plural subject

So in predicate position, adjectives can show plural marking.