Úrazové pojištění a pojištění storna cesty jsou drahá.

Because it agrees with pojištění, which is a neuter singular noun.

• pojištění = neuter
• nominative singular adjective with a neuter noun = -é

So:

• úrazové pojištění = accident insurance

Even though the whole sentence talks about two things together, this first noun phrase by itself is singular.

Here, each pojištění is singular.

That can be confusing, because pojištění has the same form in the nominative singular and nominative plural. In this sentence:

• úrazové pojištění = one type of insurance
• pojištění storna cesty = another type of insurance

So the two noun phrases are singular individually, but together they form a compound subject, which is why the verb is plural: jsou.

Because the two parts are not built in exactly the same way.

• úrazové pojištění = adjective + noun
• pojištění storna cesty = noun + genitive phrase

If you removed the second pojištění, the meaning would change or become awkward. Czech needs it here to show that the second item is also a kind of insurance.

So the sentence is structurally:

• [úrazové pojištění] a [pojištění storna cesty]

not

• [úrazové] a [storna cesty] pojištění

Because storna is the genitive singular form of storno.

The phrase pojištění storna cesty literally works like:

• insurance of cancellation of a trip

After pojištění, Czech often uses the genitive to say what is being insured:

• pojištění čeho? = insurance of what?
• pojištění storna = insurance of cancellation

So storno changes to storna.

For the same reason: it depends on storna and is also in the genitive singular.

You can think of the structure as:

• pojištění → of what? → storna
• storna → of what? → cesty

So:

• cesta = trip/journey
• cesty = of the trip

This kind of “chain of of” is very common in Czech.

Because the subject is made of two items joined by a (and):

• Úrazové pojištění
• pojištění storna cesty

Together, they form a plural subject, so the verb must also be plural:

• jsou = are

If there were only one item, you would use je:

• Úrazové pojištění je drahé.
• Pojištění storna cesty je drahé.

Because the predicate adjective agrees with a neuter plural subject.

Both head nouns are pojištění, which is neuter. When the two neuter nouns are joined together, the result is plural, and the adjective becomes neuter plural:

• drahá = expensive, neuter plural

Compare:

• pojištění je drahé = the insurance is expensive
• pojištění a pojištění jsou drahá = the insurances are expensive

So the contrast is:

• singular neuter: drahé
• plural neuter: drahá

Because Czech does not normally use articles.

So where English says:

• the insurance
• an insurance policy

Czech usually just uses the noun itself, and the meaning is understood from context.

That is why the sentence simply begins with:

• Úrazové pojištění a pojištění storna cesty...

with no separate word for the.

No. Czech word order is fairly flexible, although this version is the most neutral and natural for a plain statement.

Neutral order:

• Úrazové pojištění a pojištění storna cesty jsou drahá.

You could change the order for emphasis, for example:

• Drahá jsou úrazové pojištění a pojištění storna cesty.

That would sound more marked, as if stressing expensive. So the original sentence is the best basic version for a learner to remember.

Yes, especially in formal, travel, or insurance-related language.

It is a compact way to say trip cancellation insurance. Czech often uses this kind of genitive structure in official or business language.

Depending on context, you might also see similar expressions such as:

• pojištění storna zájezdu = cancellation insurance for a package tour
• pojištění pro případ storna cesty = insurance in case of trip cancellation

But pojištění storna cesty is perfectly natural and grammatical.