Chci pojištění zavazadel a pojištění odpovědnosti.

Chci means I want. It is the 1st person singular present tense form of the verb chtít.

So:

• chtít = to want
• chci = I want

This is a very common verb, but its forms are a bit irregular, so it is worth memorizing.

After chci, Czech normally uses the accusative case for the thing wanted.

Here, pojištění is a neuter singular noun, and its nominative and accusative forms are the same:

• pojištění = nominative singular
• pojištění = accusative singular

So even though it is in the accusative here, the form does not change.

Because after pojištění, Czech usually uses the genitive case to say what kind of insurance it is.

So:

• pojištění zavazadel = insurance of luggage / baggage insurance
• pojištění odpovědnosti = insurance of liability / liability insurance

The dictionary forms are:

• zavazadlo = a piece of luggage
• odpovědnost = responsibility, liability

But in the sentence they become:

• zavazadel = genitive plural
• odpovědnosti = genitive singular

Because Czech usually expresses this idea differently from English.

English often says:

• insurance for luggage
• insurance for liability

Czech commonly uses:

• pojištění + genitive

So it is structurally closer to:

• insurance of luggage
• insurance of liability

That is the normal and natural pattern in Czech.

Repeating pojištění makes the sentence clearer and more natural in formal or service-related contexts.

So:

• Chci pojištění zavazadel a pojištění odpovědnosti. = very clear
• Chci pojištění zavazadel a odpovědnosti. = possible, but less clear and a bit compressed

With the repeated noun, it is obvious that these are two separate types of insurance.

Yes. A is the standard Czech word for and.

Here it simply joins two noun phrases:

• pojištění zavazadel
• pojištění odpovědnosti

So the structure is:

• X a Y = X and Y

Because they refer to different kinds of things.

• zavazadla means luggage/baggage, which is naturally thought of as multiple items
• odpovědnost means liability, which is an abstract singular concept

So Czech uses:

• zavazadel = genitive plural
• odpovědnosti = genitive singular

That is normal and idiomatic.

A rough English-friendly pronunciation is:

Chci pojištění zavazadel a pojištění odpovědnosti
≈ kh-tsee po-yi-sh-tyeh-nyee za-va-za-del a po-yi-sh-tyeh-nyee od-po-vyed-nos-ti

A few useful points:

• ch is like the sound in Scottish loch or German Bach
• c is pronounced ts
• j is pronounced like English y
• stress in Czech is usually on the first syllable of each word

So:

• Chci ≈ kh-tsee
• pojištění ≈ PO-yi-sh-tyeh-nyee
• zavazadel ≈ ZA-va-za-del
• odpovědnosti ≈ OD-po-vyed-nos-ti

Yes. It is direct, clear, and perfectly normal.

Czech often sounds more direct than English, especially in practical situations like travel, insurance, or customer service.

If you want to sound softer or more polite, you could say:

• Chtěl bych pojištění zavazadel a pojištění odpovědnosti. if you are male
• Chtěla bych pojištění zavazadel a pojištění odpovědnosti. if you are female

That means something like I would like baggage insurance and liability insurance.

To some extent, yes, because Czech word order is flexible. But the original order is the most neutral and natural:

• Chci pojištění zavazadel a pojištění odpovědnosti.

You could move things around for emphasis, but that is less basic and less natural for a learner.

So as a beginner, it is best to keep this order:

• Chci
  • what you want

Because Czech does not use articles like English does.

So where English says:

• I want the insurance
• I want an insurance policy

Czech can simply say:

• Chci pojištění

The exact meaning depends on context. In this sentence, it naturally means the speaker wants those types of insurance, without needing an article.