A bankszámlakivonat itt van.

A is the definite article, equivalent to English the.

A few useful points:

• Hungarian has no grammatical gender, so the same article is used regardless of whether the noun would be masculine, feminine, or neuter in other languages.
• Hungarian uses a before consonant sounds and az before vowel sounds.

Since bankszámlakivonat starts with b, the correct article is a.

Because Hungarian very often makes compound nouns by joining words together into a single written word.

What English expresses as bank account statement or bank statement, Hungarian can package into one compound noun:

• bank
• számla
• kivonat

This is completely normal in Hungarian, even when the resulting word looks long to an English speaker.

It can be understood as:

• bank = bank
• bankszámla = bank account
• kivonat = extract, statement

So bankszámlakivonat is literally something like bank-account statement/extract.

In normal English, the natural translation is simply bank statement.

That is a very common question, because both ideas are true in different situations.

Hungarian often omits van in the present tense when one noun or adjective is linked to the subject:

• A számla új. = The bill/account is new.
• A kivonat fontos. = The statement is important.

But in location sentences, Hungarian normally keeps van:

• itt van = is here
• otthon van = is at home
• az asztalon van = is on the table

So in A bankszámlakivonat itt van, van is needed because the sentence says where something is.

Itt means here.

It is a basic adverb of place. Some useful comparisons:

• itt = here
• ott = there
• ide = to here
• oda = to there

So itt van literally means is here.

Yes, absolutely. Both are grammatical, but the emphasis changes.

• A bankszámlakivonat itt van.
  The topic is the bank statement; you are saying where it is.

• Itt van a bankszámlakivonat.
  This puts more emphasis on here, and can feel closer to Here is the bank statement or The bank statement is here.

Hungarian word order is flexible, but it is not random: it often reflects topic and focus/emphasis.

Because in standard Hungarian, a location sentence like this normally needs van.

Without van, the sentence sounds incomplete. The omission of van in the present tense only happens in certain sentence types, and location is not usually one of them.

So:

• A bankszámlakivonat új. = correct without van
• A bankszámlakivonat itt van. = correct with van

A rough English-friendly guide would be:

BANK-saam-la-ki-vo-nat

A few important spelling facts:

• sz is pronounced like English s
• s by itself is pronounced like English sh
• á is a long vowel
• Hungarian stress normally falls on the first syllable

So the stress is on BANKszámlakivonat.

Usually, yes, but not always in a one-to-one way.

In this sentence, a works just like English the. But more generally:

• Hungarian article usage does not always match English perfectly.
• Hungarian has only one definite article system, with the forms a and az, chosen by sound rather than gender.
• English and Hungarian sometimes differ in when they use or omit the article.

Still, in A bankszámlakivonat itt van, translating a as the is exactly right.

It is basically neutral, standard Hungarian.

Nothing in it is especially formal, informal, or slangy. It would sound normal in everyday speech and writing if you are simply stating that the bank statement is here.

The noun bankszámlakivonat is a fairly formal-looking word only because it is long and specific, not because the grammar of the sentence is formal.