De verzekeraar keert de herstelkosten uit.

Because uitkeren is a separable verb in Dutch.

• The full verb is uitkeren.
• In a main clause, the finite verb moves to the second position, and the particle uit goes to the end:
  • De verzekeraar keert de herstelkosten uit.
• In an infinitive or in some other verb forms, it stays together:
  • De verzekeraar wil de herstelkosten uitkeren.
• In a subordinate clause, it also stays together:
  • ... omdat de verzekeraar de herstelkosten uitkeert.

This is very common in Dutch and often feels similar to English phrasal verbs like pay out.

They are close, but not exactly the same.

• betalen = to pay
• uitkeren = to pay out, to disburse, often in a formal or financial/insurance context

With insurance, uitkeren is especially common because it suggests an official payout after a claim. So in this sentence, keert ... uit sounds more natural and more specific than just betaalt.

Because kosten is a plural noun, and plural nouns in Dutch take de.

• singular: de kost is not the usual word here
• plural: de kosten = the costs / the expenses

So:

• de herstelkosten = the repair costs

Even if you do not know the gender of the base noun, plural nouns use de.

Dutch often uses kosten in the plural to mean costs or expenses, just like English often does.

So herstelkosten literally means:

• herstel = repair / restoration
• kosten = costs

Together: repair costs

Even if English might sometimes say the cost of repairs, Dutch naturally uses the plural compound herstelkosten.

It is a compound noun, which is very common in Dutch.

It is made from:

• herstel = repair, restoration
• kosten = costs

So:

• herstelkosten = repair costs

Dutch often combines nouns into one word where English uses multiple words. Compare:

• ziekenhuis = hospital
• autoverzekering = car insurance
• herstelkosten = repair costs

• verzekeraar = insurer, insurance company
• verzekering = insurance, or an insurance policy

So:

• De verzekeraar = the insurer
• De verzekering = the insurance / the policy

That distinction is important. In this sentence, the subject is the company or institution that pays out, so verzekeraar is the right word.

Dutch main clauses usually follow the V2 rule, which means the finite verb comes in the second position.

Here the structure is:

• De verzekeraar = subject
• keert = finite verb
• de herstelkosten = object
• uit = separable particle

So the sentence pattern is:

• Subject + finite verb + object + particle

This is why you get:

• De verzekeraar keert de herstelkosten uit.

and not:

• De verzekeraar uitkeert de herstelkosten. in a main clause

Yes. You can say what is paid out, and also to whom.

For example:

• De verzekeraar keert de schadevergoeding uit. = The insurer pays out the compensation.
• De verzekeraar keert de schadevergoeding aan de klant uit. = The insurer pays out the compensation to the customer.

In your sentence, de herstelkosten is the thing being paid out.

Dutch often uses the present tense for:

• general facts
• standard procedures
• formal statements
• things that happen as part of a process

So De verzekeraar keert de herstelkosten uit can sound like:

• this is what the insurer does
• this is the next step in the claims process
• the insurer is paying out the repair costs

The simple present in Dutch can often cover what English expresses with either the present simple or present continuous, depending on context.

In a subordinate clause, the separable verb is normally written as one word again: uitkeert.

For example:

• Ik weet dat de verzekeraar de herstelkosten uitkeert. = I know that the insurer pays out the repair costs.

So compare:

• main clause: De verzekeraar keert de herstelkosten uit.
• subordinate clause: ... dat de verzekeraar de herstelkosten uitkeert.

That is a very common pattern with separable verbs in Dutch.