U slučaju da polisa osiguranja ne važi, nema naknade štete.

U slučaju da means in the event that / in case.

It is a fixed expression:

• u slučaju = in the case / in the event
• da introduces the following clause

So u slučaju da polisa osiguranja ne važi literally means something like in the event that the insurance policy is not valid.

In Serbian, da is very commonly used to introduce subordinate clauses. After expressions like u slučaju da, it is the normal choice.

Yes, you could say:

Ako polisa osiguranja ne važi, nema naknade štete.

That would also be correct and natural.

The difference is mostly in style:

• ako = plain if
• u slučaju da = more formal, administrative, legal, or contractual sounding

Because this sentence sounds like insurance or legal language, u slučaju da fits very well.

Because the subject is singular: polisa.

• polisa = policy (singular)
• važi = is valid / applies for he/she/it or a singular noun
• važe would be used with a plural subject

Compare:

• Polisa važi. = The policy is valid.
• Polise važe. = The policies are valid.

So in your sentence, polisa osiguranja is singular, so važi is the correct form.

Yes. In this sentence, važi means is valid / is in force / applies.

A very close alternative is:

• polisa osiguranja nije važeća

That also means the insurance policy is not valid.

The difference is mostly one of wording:

• ne važi often sounds like does not apply / is not valid / is no longer in force
• nije važeća is more adjectival: is not valid

In legal, official, and everyday use, both are common depending on context.

Because nema is a very common Serbian way to say there is no / there are no.

So:

• nema naknade štete = there is no damage compensation / no compensation for the damage

This is very idiomatic and natural.

You could say ne postoji naknada štete, but that would usually sound less natural here, and a bit more abstract. In legal or practical statements about entitlement, nema is the normal choice.

Because after nema (the negative form of ima, there is/are), Serbian normally uses the genitive case.

So:

• ima naknada would not be right here
• nema naknade is correct

This is a very important pattern:

• Ima vremena. = There is time.
• Nema vremena. = There is no time.
• Ima novca. = There is money.
• Nema novca. = There is no money.

So naknade is genitive singular after nema.

Štete is also in the genitive singular.

The phrase naknada štete means compensation for damage or damage compensation.

Here:

• naknada = compensation
• štete = of damage

This is a noun + noun structure where the second noun often goes into the genitive in Serbian.

So:

• naknada štete = compensation of damage / compensation for damage

Then, because the whole phrase comes after nema, the first noun also changes:

• nominative: naknada štete
• after nema: nema naknade štete

So in the full sentence:

• naknade = genitive singular, required by nema
• štete = genitive singular, because it depends on naknada

Polisa osiguranja means insurance policy.

• polisa = policy
• osiguranja = of insurance

So osiguranja is in the genitive singular. This is how Serbian commonly builds noun phrases like X of Y.

Compare:

• polisa osiguranja = insurance policy
• ugovor o radu = employment contract
• cena goriva = price of fuel

So literally, polisa osiguranja is policy of insurance, which English expresses as insurance policy.

Because Serbian has no articles like English a/an/the.

So Serbian simply says:

• polisa osiguranja
• naknade štete

Whether something means a policy, the policy, an insurance policy, or the insurance policy depends on context.

That is very normal in Serbian, and learners from English often notice it right away.

The comma separates the conditional clause from the main clause.

Structure:

• U slučaju da polisa osiguranja ne važi = subordinate clause
• nema naknade štete = main clause

This is similar to English:

• If the policy is not valid, there is no compensation for the damage.

In Serbian, when this kind of dependent clause comes first, a comma is normally used before the main clause.

The given word order is natural and appropriate, especially in formal language.

You could also reverse the two parts:

• Nema naknade štete u slučaju da polisa osiguranja ne važi.

This still means the same thing.

The difference is mainly emphasis:

• starting with U slučaju da... highlights the condition first
• starting with Nema naknade štete... highlights the result first

Both are grammatical, but the original sentence sounds very natural for official or legal wording.