A bankfiók vezetője itt van.

A is the Hungarian definite article, so it means the.

Hungarian has two forms of the definite article:

• a before a consonant
• az before a vowel

So:

• a bankfiók = the bank branch
• az iskola = the school

In this sentence, bankfiók starts with b, so Hungarian uses a.

Hungarian often forms compound nouns by writing them as a single word.

• bank = bank
• fiók = branch, sub-office

So bankfiók means bank branch.

This is very normal in Hungarian. English often uses two words where Hungarian prefers one compound word.

Vezető means leader, head, or manager.

The form vezetője means his/her/its manager or the manager of it.

Here’s the important point: Hungarian often shows possession with a suffix on the possessed noun.

• vezető = manager
• vezetője = its manager / the manager of it

In this sentence, vezetője refers back to a bankfiók, so:

• a bankfiók vezetője = the manager of the bank branch

The ending -je is a possessive ending.

Hungarian usually does not use a separate word like English of in this kind of phrase.

Instead, it often uses this pattern:

possessor + possessed noun with a possessive suffix

So:

• a bankfiók vezetője literally: the bank branch its-manager natural English: the manager of the bank branch

This is one of the most important Hungarian structures to learn.

A few similar examples:

• a ház ajtaja = the door of the house
• az autó színe = the color of the car
• a cég igazgatója = the director of the company

Because the whole phrase acts as one definite noun phrase:

• a bankfiók vezetője = the manager of the bank branch

In Hungarian possessive constructions like this, the article usually goes before the possessor:

• a bankfiók vezetője
• az iskola tanára
• a város polgármestere

You do not normally say something like a bankfiók a vezetője for this meaning.

Itt means here.

Van is the 3rd person singular form of lenni, the verb to be.

So:

• itt van = is here

In this sentence:

• A bankfiók vezetője itt van.
• The manager of the bank branch is here.

Hungarian often uses van in location statements like this:

• Itt van. = He/She/It is here.
• Otthon van. = He/She/It is at home.
• A konyhában van. = He/She/It is in the kitchen.

This is a very common question.

Hungarian often omits to be in the present tense when one noun or adjective is directly equated with another:

• Ő tanár. = He/She is a teacher.
• A ház nagy. = The house is big.

But when talking about location or existence, Hungarian normally uses van:

• Itt van. = He/She/It is here.
• A szobában van. = He/She/It is in the room.

So in your sentence, van is needed because itt expresses location.

Yes, that is possible.

Both of these are grammatical:

• A bankfiók vezetője itt van.
• Itt van a bankfiók vezetője.

The difference is mainly one of focus and information structure.

• A bankfiók vezetője itt van.
  This starts with the subject: the bank branch manager is here.

• Itt van a bankfiók vezetője.
  This puts more emphasis on here or on the fact that the person has arrived / is present: the bank branch manager is here or here is the bank branch manager.

Hungarian word order is flexible, but it is not random. It often reflects what is already known and what is being emphasized.

A rough pronunciation guide for an English speaker is:

• A = short aw
• bankfiók ≈ bawnk-fee-ohk
• vezetője ≈ veh-zeh-tur-yeh
• itt van ≈ eett vawn

A few useful pronunciation notes:

• a in Hungarian is usually like o in British hot
• ó is a long vowel
• ő is a long front rounded vowel, something like German ö, if you know it
• j is pronounced like English y
• tt is a long consonant, held a bit longer than a single t

So vezetője ends with -je, pronounced roughly -yeh, not like English jay.

In form, vezetője is a possessed noun: his/her/its manager.

But in a phrase like a bankfiók vezetője, it naturally means the manager of the bank branch.

So even though the suffix historically and grammatically looks like its manager, the whole phrase is simply the standard Hungarian way to say:

• the branch manager
• the manager of the bank branch

You should understand it as a normal possessive construction, not as something unusually personal.

Yes. Vezető is a broad word.

Depending on context, it can mean:

• leader
• head
• manager
• person in charge

In a business context like bankfiók, manager is usually the most natural English translation.

So:

• A bankfiók vezetője itt van. most naturally = The manager of the bank branch is here.

But the exact English word can vary depending on context.