Naše babička má v pokoji nový polštář a teplou deku.

Naše means our, and it has to agree with babička.

• babička = a feminine singular noun
• so náš changes to naše

A few forms of náš are:

• náš = masculine singular
• naše = feminine singular and also neuter singular in some contexts
• naši = masculine animate plural or sometimes other case forms

So naše babička = our grandmother.

Má is the 3rd person singular form of mít = to have.

So:

• já mám = I have
• ty máš = you have
• on/ona má = he/she has

Since babička is she, Czech uses má.

After v meaning in, Czech usually uses the locative case when talking about location.

• pokoj = room
• v pokoji = in the room

So the noun changes because of the preposition:

• pokoj → basic form
• v pokoji → locative singular

This is very common in Czech:

• v domě = in the house
• v autě = in the car
• v pokoji = in the room

Because deku is the accusative singular form of deka.

In this sentence, the blanket is a direct object of má:

• she has what? → deku

For many feminine nouns ending in -a, the accusative singular changes to -u:

• deka → deku
• kniha → knihu
• taška → tašku

So teplou deku is the correct form for a warm blanket as the object.

Because they belong to different noun genders and declension patterns.

• polštář is masculine inanimate
• deka is feminine

In the accusative singular:

• masculine inanimate nouns often look the same as the nominative
• many feminine nouns ending in -a change to -u

So:

• nový polštář = accusative singular, but it looks the same as nominative
• teplou deku = accusative singular, and both words change form

Because adjectives must agree with the noun in:

• gender
• number
• case

Here both nouns are direct objects, so both are in the accusative singular, but their genders are different:

• polštář = masculine inanimate
  → nový polštář
• deka = feminine
  → teplou deku

So the adjective endings are different because the nouns are different.

Yes. A means and.

So:

• nový polštář a teplou deku = a new pillow and a warm blanket

It simply joins the two objects.

Czech does not use articles like English a/an and the.

So:

• polštář can mean a pillow or the pillow
• deku can mean a blanket or the blanket

The exact meaning depends on context. In a basic translation, this sentence is usually understood as a new pillow and a warm blanket, but Czech itself does not have separate article words.

Yes, Czech word order is more flexible than English.

This sentence is neutral and natural:

• Naše babička má v pokoji nový polštář a teplou deku.

But you could also hear:

• V pokoji má naše babička nový polštář a teplou deku.
• Nový polštář a teplou deku má naše babička v pokoji.

The basic meaning stays the same, but the emphasis changes.

• starting with V pokoji emphasizes the location
• starting with Nový polštář a teplou deku emphasizes what she has

Not necessarily. Pokoj usually means room in a general sense.

So v pokoji most directly means in the room.

If you specifically want bedroom, Czech more often uses:

• ložnice = bedroom

So this sentence does not automatically mean bedroom unless the context makes that clear.

A rough guide:

• š sounds like English sh
• ř is a special Czech sound with no exact English equivalent

So polštář is approximately:

• pol-shtaarzh as a rough learner-friendly approximation

More precisely:

• pol like pole without the final e
• št like sht
• long á = a longer a
• ř is the tricky Czech sound, something between r and zh

Learners often need time with ř, and that is completely normal.

Yes, very common.

Czech often uses mít = to have just like English:

• Mám knihu. = I have a book.
• Má auto. = He/She has a car.
• Naše babička má v pokoji nový polštář a teplou deku.

So this sentence is a very standard and natural way to say that someone has something in a certain place.