W nowym mieszkaniu jest jeszcze jeden wolny pokój dla gości.

Because after w when it means in, Polish normally uses the locative case.

So:

• mieszkanie = apartment, flat
• w mieszkaniu = in the apartment

The adjective also has to match:

• nowe mieszkanie = a new apartment
• w nowym mieszkaniu = in a new apartment

So both words change because they are in the locative singular.

It is the locative singular.

You can think of it like this:

• base form: nowe mieszkanie
• after w = w nowym mieszkaniu

The noun mieszkanie is neuter, so in the locative singular it becomes mieszkaniu, and the adjective nowe becomes nowym to agree with it.

Jest means is and comes from być = to be.

In this sentence, jest is used to say that something exists or is present somewhere:

• W nowym mieszkaniu jest... = In the new apartment there is...

This is a very common Polish structure for there is / there are.

Even though English often uses there is, Polish usually just uses jest.

Because the main thing being talked about is singular:

• jeden pokój = one room

So Polish uses singular jest.

Compare:

• Jest jeden pokój. = There is one room.
• Są dwa pokoje. = There are two rooms.

Even though the sentence contains several words, the grammatical subject is still jeden wolny pokój, which is singular.

Jeszcze jeden means one more, another one, or an additional one, depending on context.

Here it suggests that besides other rooms, there is one more free room.

Examples:

• Mam jeszcze jeden pomysł. = I have one more idea.
• Czy jest jeszcze jedna kawa? = Is there another coffee?

So in this sentence, jeszcze adds the idea of in addition.

All three words are in the nominative singular masculine because they describe the same noun:

• jeden = one
• wolny = free / available
• pokój = room

They must agree with one another:

• masculine singular nominative: jeden wolny pokój

If the noun changed, the other words would change too. For example:

• jedno wolne mieszkanie = one free apartment
• jedna wolna sofa = one free sofa

Because pokój is the subject-like noun in this jest structure, so it stays in the nominative.

In this sentence:

• jest jeden wolny pokój = there is one free room

That is why you get pokój, not pokoju.

You would see pokoju in other cases, for example:

• Nie ma pokoju. = There is no room / There is no room available.
• Szukam pokoju. = I am looking for a room.

So the form changes depending on its grammatical role.

Because dla requires the genitive case.

The basic form is:

• goście = guests

After dla it becomes:

• dla gości = for guests

So:

• pokój dla gości = a room for guests

This is a very common pattern:

• dla dzieci = for children
• dla rodziny = for the family
• dla studentów = for students

Not exactly. Wolny usually means free, available, or unoccupied.

So wolny pokój here means a room that is available to use.

Sometimes English might translate it as vacant room, spare room, or free room, depending on context.

If you wanted to emphasize that a room is physically empty, Polish might use words like:

• pusty pokój = an empty room

So wolny is more about availability than about having no furniture or objects in it.

Yes, Polish word order is quite flexible.

The sentence:

• W nowym mieszkaniu jest jeszcze jeden wolny pokój dla gości.

is natural and neutral. It starts with the place, then says what exists there.

You could also hear variations like:

• Jeszcze jeden wolny pokój dla gości jest w nowym mieszkaniu.
• W nowym mieszkaniu jeszcze jest jeden wolny pokój dla gości.

But the original version sounds the most natural in ordinary description.

In Polish, word order often changes for focus, emphasis, or style, not just for grammar.

It tells us what kind of room it is or who it is intended for.

So:

• pokój = room
• pokój dla gości = room for guests / guest room

It works like a descriptive phrase attached to pokój.

This is a very common way in Polish to express purpose:

• karta dla klienta = card for the customer
• prezent dla mamy = present for mum
• miejsce dla dzieci = place for children

Most naturally, they would understand it as a guest room or a room intended for guests.

Polish often uses a longer phrase where English might prefer a compound noun:

• pokój dla gości = guest room
• literally: room for guests

So it is very natural Polish, even though English compresses the idea more.

Polish does not have articles like a and the, so the phrase itself does not explicitly mark that difference.

• w nowym mieszkaniu can mean in a new apartment
• or in the new apartment

The exact meaning depends on context.

This is normal in Polish. The listener figures out from the situation whether the speaker means a specific apartment or just any new apartment.