Pojištění zavazadel a úrazové pojištění jsou důležitá.

Because pojištění often takes the genitive to mean insurance of / insurance for something.

• basic form: zavazadla = luggage / baggage
• genitive plural: zavazadel

So:

• pojištění zavazadel = luggage insurance
• literally: insurance of baggage

This is a very common Czech pattern: noun + genitive.

Czech often repeats the noun when two different types are being listed clearly:

• Pojištění zavazadel a úrazové pojištění

This sounds natural and unambiguous. In English, we often avoid repetition more strongly, but Czech is more comfortable repeating a noun if it helps clarity.

If you removed the second pojištění, the sentence would sound incomplete or at least less natural in this structure.

Because the subject is two things joined by a (and):

• pojištění zavazadel
• úrazové pojištění

Each one is grammatically singular, but together they make a plural subject, so the verb must be plural:

• jsou = are

Compare:

• Úrazové pojištění je důležité. = Accident insurance is important.
• Pojištění zavazadel a úrazové pojištění jsou důležitá. = Luggage insurance and accident insurance are important.

This is a very common learner question. The reason is that the predicate adjective agrees with the whole subject.

Here, the two items together are treated as neuter plural, and the nominative plural neuter form of důležitý is:

• důležitá

A quick comparison:

• důležité = neuter singular
• důležitá = neuter plural

So:

• Pojištění je důležité. = Insurance is important.
• Pojištění ... a ... pojištění jsou důležitá. = ... insurance and ... insurance are important.

This neuter plural in -á is one of those forms that often surprises English speakers.

It is in the nominative singular.

Why?

Because it is part of the subject of the sentence:

• Pojištění zavazadel a úrazové pojištění = the subject

Inside that phrase:

• pojištění is a neuter singular noun
• úrazové is an adjective agreeing with it, so it is also neuter singular nominative

So:

• úrazové pojištění = accident insurance

Because Czech has more than one natural way to describe a type of insurance.

1. noun + genitive

   • pojištění zavazadel = insurance of baggage / luggage insurance

2. adjective + noun

   • úrazové pojištění = accident insurance
   • literally something like injury-related insurance

Both patterns are normal. Czech does not need to build all similar phrases in exactly the same way.

Úrazové is an adjective from úraz, which means injury or accident in the sense of a physical injury event.

So:

• úraz = injury / accident
• úrazový / úrazové = injury-related / accident-related

Therefore:

• úrazové pojištění = accident insurance

It agrees with pojištění, which is neuter singular, so the form is úrazové.

Each expression is singular by itself.

• pojištění zavazadel = one kind of insurance
• úrazové pojištění = another kind of insurance

But when you join them with a (and), the whole subject becomes plural, which is why you get:

• jsou
• důležitá

So the pattern is:

• singular + singular = plural overall

Yes. Czech word order is more flexible than English, as long as the grammar stays clear.

For example, you could also say:

• Úrazové pojištění a pojištění zavazadel jsou důležitá.

That would still mean the same thing. The difference is mostly one of emphasis or style.

The version you were given is perfectly natural, but it is not the only possible order.

Because Czech does not have articles.

English says things like:

• the insurance
• an accident
• the luggage insurance

Czech simply does not use separate words for that. Whether something is a, an, or the is understood from context.

So:

• Pojištění zavazadel a úrazové pojištění jsou důležitá.

works without any article words at all.

In careful pronunciation, it is written jsou, but in normal speech the initial j is often very weak or effectively not heard.

So learners often hear something close to:

• sou

This is normal. The spelling still remains jsou.

Not in a normal present-tense sentence like this. In standard Czech, you normally keep the present tense of být (to be):

• jsou důležitá = are important

So the correct full sentence is:

• Pojištění zavazadel a úrazové pojištění jsou důležitá.

Leaving out jsou would sound incorrect in standard Czech.

It describes both.

The whole subject is:

• Pojištění zavazadel a úrazové pojištění

Then:

• jsou důležitá = are important

So důležitá applies to the two items together, not just to the second one.