A rendőrség itt van.

A is the Hungarian definite article, equivalent to the in English.

So:

• a rendőrség = the police

Hungarian has two forms of the definite article:

• a before most consonant sounds
• az before vowel sounds

Since rendőrség begins with a consonant, it takes a.

Rendőrség means the police as an institution or body, similar to the police force or the police authorities.

• rendőr = police officer / policeman
• rendőrök = police officers / policemen
• rendőrség = police, police force, police department

So A rendőrség itt van is not literally the police officers are here; it is more like the police are here in the collective/institutional sense.

If you specifically wanted to say The police officers are here, you could say:

• A rendőrök itt vannak.

Because rendőrség is grammatically singular in Hungarian.

Even though English the police usually takes a plural verb (the police are), Hungarian treats rendőrség as a singular noun. So the verb must also be singular:

• A rendőrség itt van. = The police are here.

Compare:

• A rendőrök itt vannak. = The police officers are here.

Here rendőrök is plural, so the verb is plural too: vannak.

Itt means here.

It is a basic place adverb:

• itt = here
• ott = there

In this sentence, itt van means is here.

That is a very common and important question.

Hungarian often omits van/vannak in the present tense when the predicate is a noun or adjective:

• A rendőr fáradt. = The police officer is tired.
• Ez egy autó. = This is a car.

But when you are expressing location or existence, Hungarian normally uses van/vannak:

• A rendőrség itt van. = The police are here.
• Az autó kint van. = The car is outside.

So in this sentence, van is necessary because the sentence tells us where something is.

Yes, you can also say Itt van a rendőrség.

Both are correct, but the emphasis is slightly different.

• A rendőrség itt van.
  This starts with the police as the topic, then says where they are.

• Itt van a rendőrség.
  This puts more attention on here, often sounding like The police are here! or Here are the police.

Hungarian word order is flexible, and changing it often changes the focus or emphasis rather than the basic meaning.

Yes, it is natural.

It could be used in situations like:

• someone has called the police and they have arrived
• someone is warning others that the police are present
• someone is answering a question about whether the police have come

Depending on tone and context, it could sound neutral, reassuring, or alarming.

Yes, depending on context.

Because rendőrség refers to the police as an institution, it can sometimes feel closer to:

• the police
• the police force
• the police department / police authorities

In everyday use, though, A rendőrség itt van will often simply be understood as The police are here.

If you want to clearly refer to individual officers present at the scene, A rendőrök itt vannak is more explicit.

A helpful approximate pronunciation is:

• REN-dur-shayg

A few details:

• r is a rolled or tapped Hungarian r
• e in ren- is like e in bed
• ő is a long rounded vowel with no exact English equivalent
• s in Hungarian sounds like English sh
• é sounds like the vowel in say, but pure and longer
• g is always a hard g

So the whole sentence is approximately:

• A REN-dur-shayg itt van

Also:

• itt has a short i and a long/doubled t
• van sounds roughly like vawn, but with a short Hungarian a

Because itt is already a complete adverb meaning here.

Hungarian often uses case endings on nouns to express location, such as:

• a házban = in the house
• az asztalon = on the table

But itt and ott are special place adverbs:

• itt = here
• ott = there

So no extra ending is needed.

You would say:

• A rendőrség nincs itt.

Notice that Hungarian uses nincs as the negative form of van in the singular:

• van = is
• nincs = is not

And for plural:

• vannak = are
• nincsenek = are not

So:

• A rendőrség nincs itt. = The police aren’t here.
• A rendőrök nincsenek itt. = The police officers aren’t here.