Politiet finner drapsmannen.

In Norwegian, politiet is the definite form of politi. Grammatically, it looks like a singular neuter noun, but in meaning it often refers to the police as an institution or body of officers.

So:

• politi = police
• politiet = the police

This is different from English, where the police is always treated as plural. In Norwegian, the noun itself does not have to look plural to carry that meaning.

Norwegian usually puts definiteness at the end of the noun instead of using a separate article the way English does.

Here:

• politiet = politi
  • -et = the police
• drapsmannen = drapsmann
  • -en = the murderer

So the endings -et and -en are doing the job that English the does.

Because they belong to different grammatical genders.

• politi is a neuter noun, so its definite singular form is politiet
• drapsmann is a masculine noun, so its definite singular form is drapsmannen

Very roughly:

• neuter nouns often take -et in the definite singular
• masculine nouns often take -en in the definite singular

Finner is the present tense of å finne = to find.

So:

• å finne = to find
• finner = find / finds / is finding

In Norwegian, the present tense often covers both:

• finds
• is finding

The exact English translation depends on context.

Because Norwegian verbs do not change according to the subject the way English verbs do.

In English:

• I find
• you find
• he finds

In Norwegian, it stays the same:

• jeg finner
• du finner
• han finner
• politiet finner

So finner works for all persons in the present tense.

This is the normal Norwegian main-clause word order:

Subject + Verb + Object

So:

• Politiet = subject
• finner = verb
• drapsmannen = object

This is very similar to basic English word order:

• The police / find / the murderer

Because Norwegian makes compound nouns very freely, and they are normally written as one word.

Here:

• drap = killing / homicide
• mann = man
• drapsmann = killer / murderer
• drapsmannen = the murderer

The -s- in the middle is a common linking sound/letter in compounds. It does not usually need to be translated directly; it just helps form the compound.

Usually, yes. Drapsmann literally contains mann, so it normally refers to a male perpetrator.

If you want a more general word for murderer, Norwegian often uses morderen = the murderer.

So:

• drapsmannen = the male murderer / the killer
• morderen = the murderer, often more general

In many contexts, both can work, but drapsmannen tends to sound more specifically male.

Normally, no. Politiet usually refers to the police as a whole, not a single officer.

If you want to talk about one officer, Norwegian would usually use a different noun, such as:

• en politibetjent = a police officer
• en politimann = a policeman

So in this sentence, politiet is best understood as the police.

You add ikke after the finite verb in a normal main clause:

Politiet finner ikke drapsmannen.

That means The police do not find the murderer.

This placement is very common in Norwegian:

• subject + verb + ikke
  • rest

Yes. Norwegian usually does not have a separate everyday verb form for the English progressive is finding.

So Politiet finner drapsmannen could, depending on context, correspond to:

• The police find the murderer
• The police are finding the murderer

In practice, though, English would more naturally translate this sentence as The police find the murderer or The police have found the murderer, depending on the wider context.

Because a simple definite noun usually does not take a separate definite article before it.

So you say:

• drapsmannen = the murderer

not normally:

• den drapsmannen

However, if there is an adjective, Norwegian often uses both a separate article and a definite ending:

• den farlige drapsmannen = the dangerous murderer

So in your sentence, drapsmannen by itself is completely correct.