Die Polizei verfolgt den Täter und verhaftet ihn.

In this sentence, die Polizei is singular, not plural. The noun Polizei means police as an institution or force, and in German it is a singular feminine noun.

So:

• die Polizei = the police
• verfolgt = pursues / is pursuing (3rd person singular)

Even though English the police takes a plural verb (the police are), German treats die Polizei as singular:

• Die Polizei verfolgt ... = The police pursue ...

Because den Täter is the direct object of verfolgt.

German marks the role of nouns with cases. Here:

• die Polizei is the subject
• den Täter is the object

Täter is a masculine noun, so its article changes in the accusative case:

• nominative: der Täter
• accusative: den Täter

So after a transitive verb like verfolgen, you use the accusative:

• Die Polizei verfolgt den Täter.

Ihn is the accusative masculine singular pronoun meaning him.

It refers back to den Täter:

• den Täter = the perpetrator / offender
• ihn = him

It is used because verhaften also takes a direct object, and German avoids repeating the full noun if it is already clear:

• Die Polizei verfolgt den Täter und verhaftet ihn.

This is just like English:

• The police pursue the offender and arrest him.

Because the same subject applies to both verbs.

The sentence has two coordinated verbs:

• verfolgt
• verhaftet

They are linked by und, and the subject die Polizei is understood for both:

• Die Polizei verfolgt den Täter und verhaftet ihn.

In English, we do the same:

• The police pursue the offender and arrest him.

You could repeat the subject, but it would usually sound unnecessary:

• Die Polizei verfolgt den Täter und die Polizei verhaftet ihn.

Because und is a coordinating conjunction, not a subordinating one.

In German main clauses, the conjugated verb normally stays in the second position. With und, the second clause keeps normal main-clause word order.

So:

• Die Polizei verfolgt den Täter
• und verhaftet ihn

The second clause is essentially:

• und [die Polizei] verhaftet ihn

The subject is omitted because it is the same as before.

If this were a subordinate clause introduced by something like weil, the verb would go to the end. But und does not cause that change.

Yes, here they are present tense forms.

Both are:

• 3rd person singular present
  • verfolgen → verfolgt
  • verhaften → verhaftet

It is true that these forms also look like the past participles:

• verfolgt
• verhaftet

But the sentence structure shows they are present tense here. There is no auxiliary verb like hat or ist.

So:

• Die Polizei verfolgt den Täter und verhaftet ihn. = present tense

Compare:

• Die Polizei hat den Täter verfolgt und ihn verhaftet. = perfect tense

Because all German nouns are capitalized.

So in this sentence:

• Polizei is capitalized because it is a noun
• Täter is capitalized because it is a noun

This is a standard rule in German, not something special about these words.

Täter is masculine.

You can tell from the dictionary form:

• der Täter

That is why its forms in the sentence are:

• den Täter in the accusative
• ihn to refer back to it

Many nouns ending in -er that refer to a male person are masculine, although you should still learn the article with the noun:

• der Täter
• der Fahrer
• der Lehrer

Grammatically, it is present tense. It means something like:

• The police pursue the offender and arrest him
• or The police are pursuing the offender and arresting him, depending on context

However, German sometimes uses the present tense for vivid narration, headlines, or summaries. Still, if you simply want to describe a completed past event, German would more often use a past form, for example:

• Die Polizei verfolgte den Täter und verhaftete ihn.
• Die Polizei hat den Täter verfolgt und ihn verhaftet.

So this sentence is present tense in form, but context can affect how natural it sounds.

In a sentence like this, die Polizei is singular and refers to the police force as a whole.

If you want to talk about multiple police forces, German can use a plural, but that is much less common in everyday basic sentences. For most learner contexts, it is best to think of:

• die Polizei = singular collective noun

So:

• Die Polizei kommt. = The police are coming.
• Die Polizei verhaftet ihn. = The police arrest him.

This is one of those places where German grammar and English grammar do not match neatly.