Máme vlastní pojištění domácnosti.

Máme is the 1st person plural present tense of mít (to have).

So:

• mám = I have
• máme = we have

In this sentence, Máme means we have.

Because Czech verbs usually already show the subject in their endings.

The ending -me in máme tells you the subject is we. So Czech often leaves out the pronoun my (we) unless it is needed for emphasis.

• Máme vlastní pojištění domácnosti. = neutral, normal
• My máme vlastní pojištění domácnosti. = we have our own home insurance, maybe contrasting with someone else

The idea of our comes from vlastní plus the subject we.

vlastní means one's own. So when the subject is we, vlastní is understood as our own.

That is why:

• Máme vlastní pojištění domácnosti. = We have our own home insurance.

You could also say naše vlastní, but that sounds more emphatic:

• Máme naše vlastní pojištění domácnosti. = We have our very own home insurance.

Here vlastní means own in the sense of one's own.

So:

• vlastní auto = one's own car
• vlastní byt = one's own flat/apartment
• vlastní pojištění domácnosti = one's own home insurance

In this sentence, it does not mean private in some special legal sense, and it does not mean self-insurance. It simply means the insurance belongs to us / is arranged by us for our own home.

Yes, they are related in meaning.

• vlastnit = to own
• vlastní = own / one's own

But grammatically they are different:

• vlastnit is a verb
• vlastní is an adjective

In your sentence, vlastní describes pojištění.

Literally, it means insurance of the household/home.

In natural English, that is usually:

• home insurance
• household insurance

The noun pojištění means insurance or insurance coverage, and domácnosti tells you what the insurance is for.

So:

• pojištění domácnosti = insurance covering the home/household

Because it is in the genitive singular.

The basic form is:

• domácnost = household, home

After another noun, Czech often uses a noun + genitive structure where English uses a compound noun.

So:

• pojištění domácnosti literally = insurance of the household
• natural English = home insurance

This is a very common pattern in Czech.

Also, domácnost is a feminine noun ending in -ost, and nouns of this type usually have -i in the genitive singular:

• radost → radosti
• možnost → možnosti
• domácnost → domácnosti

It actually is the direct object, so grammatically it is in the accusative.

However, pojištění is a neuter singular noun, and for many neuter nouns the nominative and accusative singular look exactly the same.

So:

• nominative: pojištění
• accusative: pojištění

The case is different in function, but not in visible form.

Here is the structure:

• Máme = verb
• vlastní pojištění = direct object, so accusative singular
• domácnosti = dependent noun after pojištění, so genitive singular

So the core pattern is:

máme + accusative
pojištění + genitive

It can mean either, depending on context.

• household is the more literal meaning
• home is often the more natural English translation in everyday speech

In insurance language, pojištění domácnosti is a standard phrase. In English, this is usually translated as home insurance or household insurance, depending on the exact context and country.

Because Czech does not have articles.

So Czech does not directly mark the difference between:

• a home insurance policy
• the home insurance policy

That information comes from context instead.

In this sentence, natural English is simply:

• We have our own home insurance.

Trying to match English articles word-for-word would not work, because Czech does not use them.

No, Czech word order is fairly flexible.

The sentence as given:

• Máme vlastní pojištění domácnosti.

is a neutral, natural way to say it.

If you change the order, the basic meaning can stay similar, but the emphasis changes. For example:

• Vlastní pojištění domácnosti máme. = We do have our own home insurance. / As for home insurance, we have our own.
• Pojištění domácnosti máme vlastní. = possible, but less neutral and more marked

So the original order is the best standard version for most situations.

Not normally.

Máme vlastní pojištění domácnosti. means:

• We have our own home insurance.

It is about having insurance coverage, not about the action of insuring something yourself.

If you wanted to express we insure it ourselves, you would need a different Czech structure, for example something with pojistit or pojišťovat plus sami.