Politiet starter etterforskningen.

Because Norwegian often puts the definite article at the end of the noun instead of using a separate word like English the.

• politi = police
• politiet = the police

So -et here marks the noun as definite.

This is very common in Norwegian:

• bil = car
• bilen = the car

With politiet, the whole word means the police.

Grammatically, it is usually treated as a singular collective noun in Norwegian.

That is different from English, where the police often behaves like a plural idea:

• English: The police are...
• Norwegian: Politiet er... / Politiet starter...

So even though politiet refers to a group of people, the grammar in Norwegian is singular here.

Starter is the present tense form of the verb å starte.

• infinitive: å starte = to start
• present tense: starter = start / starts

In Norwegian, present tense verbs often end in -r:

• snakker = speak / speaks
• kommer = come / comes
• starter = start / starts

Unlike English, Norwegian verbs do not change depending on the subject:

• jeg starter = I start
• du starter = you start
• politiet starter = the police start(s)

The verb form stays the same.

For the same reason as politiet: Norwegian usually adds definiteness as a suffix.

• etterforskning = investigation
• etterforskningen = the investigation

So the sentence literally looks like:

• Politiet = the police
• starter = start
• etterforskningen = the investigation

This attached definite ending is one of the most important differences from English noun structure.

The base form is etterforskning, which means investigation.

Here is the breakdown:

• etterforskning = investigation
• etterforskningen = the investigation

This noun is feminine or masculine in Bokmål depending on style, but in many standard forms you will often see the definite form etterforskningen.

Because Norwegian usually expresses the by adding an ending to the noun.

So instead of saying something like:

• the police
• the investigation

Norwegian says:

• politi-et
• etterforskning-en

That is the normal pattern for definite nouns.

A separate determiner can appear in some other structures, especially with adjectives:

• etterforskningen = the investigation
• den nye etterforskningen = the new investigation

But in your sentence, no separate word is needed.

No, this is very straightforward Subject–Verb–Object word order:

• Politiet = subject
• starter = verb
• etterforskningen = object

So it matches basic English order:

• The police start the investigation.

This makes the sentence relatively easy for English speakers.

Yes, that is possible, and it would also mean something like The police begin the investigation.

The difference is mostly nuance:

• starte = start
• begynne = begin

In many contexts they are both natural. Starte can sound a little more like launch/initiate, while begynne is a very general begin.

So:

• Politiet starter etterforskningen = The police start/launch the investigation.
• Politiet begynner etterforskningen = The police begin the investigation.

By itself, starter is present tense, but Norwegian present tense can sometimes refer to the near future too, depending on context.

So this sentence could mean:

• The police are starting the investigation
• The police start the investigation
• The police will start the investigation

However, without more context, many learners should understand it first simply as a present-tense statement: The police start / are starting the investigation.

A rough English-friendly approximation is:

po-lee-TEE-et STAR-ter ET-ter-forsk-ning-en

A few notes:

• politiet has stress near the end: poliTIet
• starter has a clear r sound at the end
• etterforskningen is a long compound word, so it helps to hear the parts:
  • etter
  • forskning
  • -en

An exact pronunciation depends somewhat on dialect, but that breakdown can help you recognize the words when listening.