Az okirat érvényes.

Both a and az mean the in Hungarian. Which one you use depends on the sound at the beginning of the next word:

• a before a consonant: a ház
• az before a vowel: az okirat

Since okirat begins with o, the correct form is az.

Okirat is a fairly formal word. It usually means an official document, especially a legal or certified one.

It is more specific and formal than some other Hungarian words:

• irat = paper, document, record
• dokumentum = document
• okirat = official/legal document, deed, instrument

So this sentence sounds more formal than if it used dokumentum.

Here, érvényes is not directly modifying the noun inside a noun phrase. It is the predicate of the sentence.

So:

• érvényes okirat = a valid document
  
  • here érvényes comes before the noun
• Az okirat érvényes. = The document is valid.
  
  • here érvényes comes after the noun because it is saying something about the subject

This is similar to the difference between:

• a red car
• the car is red

Nothing is missing. In Hungarian, in the present tense, the verb to be is usually left out in the third person singular and third person plural when the predicate is a noun, adjective, or similar expression.

So:

• Az okirat érvényes. = The document is valid.

But in other persons, the verb appears:

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

So the missing is is completely normal Hungarian grammar.

It is in the nominative form, which is the basic dictionary form. Hungarian usually leaves the subject unmarked.

So okirat here is simply the subject: the document.

If it were a direct object, it would usually take -t:

• az okiratot = the document as an object

For example:

• Látom az okiratot. = I see the document.

No. Hungarian has no grammatical gender, so adjectives do not change for masculine, feminine, or neuter.

So érvényes stays the same regardless of who or what is being described:

• A szerződés érvényes. = The contract is valid.
• A bizonyítvány érvényes. = The certificate is valid.

However, Hungarian can show plural in predicate adjectives:

• Az okiratok érvényesek. = The documents are valid.

So there is number agreement, but not gender agreement.

It would be:

• Az okiratok érvényesek.

Breakdown:

• az = the
• okiratok = documents
• érvényesek = are valid / valid (plural predicate form)

A useful contrast:

• érvényes okiratok = valid documents
  
  • adjective before the noun, no plural ending on the adjective
• Az okiratok érvényesek. = The documents are valid.
  
  • predicate adjective, plural ending -ek

Yes. Hungarian word order is quite flexible, but different orders can sound more neutral or more emphatic.

The neutral sentence is:

• Az okirat érvényes.

You may also see:

• Érvényes az okirat.

That version gives more focus to érvényes, something like:

• The document is valid
• or It is valid, the document

So the basic meaning is similar, but the information structure changes.

You add nem before the predicate:

• Az okirat nem érvényes.

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

Approximately:

• ér sounds like a long ayr
• vé has a long e sound
• ny is like the ny in canyon
• s in Hungarian is pronounced like English sh

So érvényes is roughly:

• AIR-vay-nyesh

And okirat is roughly:

• O-kee-rat

Also remember that Hungarian stress is normally on the first syllable of each word:

• AZ O-ki-rat ÉR-vé-nyes

Yes. That means This document is valid.

• Az okirat érvényes. = The document is valid.
• Ez az okirat érvényes. = This document is valid.

The second version is more specific or contrastive, especially if you are distinguishing it from other documents.