A hálószoba ablaka zárva van, ezért reggel meleg marad a szoba.

Both are possible, but a hálószoba ablaka is the more neutral, compact way to say the bedroom window.

Hungarian usually shows possession like this:

possessor + possessed noun with a possessive ending

So:

hálószoba ablaka
literally: bedroom its-window

The longer version, a hálószobának az ablaka, is also correct, but it is more explicit or emphatic. English often uses of or 's, but Hungarian usually prefers this possessive structure instead.

The -a is a 3rd person singular possessive suffix.

• ablak = window
• ablaka = his/her/its window

In this sentence, the its refers to the bedroom, so a hálószoba ablaka means the bedroom's window.

This is a very common Hungarian pattern. The possessed thing gets the possessive ending, not the possessor.

Hungarian possessive endings are not always the same for every noun. Some nouns take -a/-e, and some take -ja/-je.

For ablak, the correct form is:

• ablak → ablaka

not ablakja

Unfortunately, this is something learners partly have to get used to noun by noun, although there are patterns. Compare:

• asztal → asztala
• ablak → ablaka
• kert → kertje

So the form in the sentence is simply the correct possessive form of ablak.

zárva van means is closed or is in a closed state.

It is made from:

• zárva = a participle-like form from zárni = to close
• van = is

Together, they describe a state, not an action.

So:

• Az ablak zárva van = The window is closed
• Valaki bezárja az ablakot = Someone closes the window

This is not quite the same as an English passive. It is more like saying that something is in a closed condition.

Because the two clauses use different kinds of predicates.

In zárva van, the real state word is zárva, and van is needed as the finite verb:

• zárva van = is closed

But in meleg marad a szoba, the verb is already marad:

• marad = stays, remains

So marad does the job that van would do in a simple equational sentence.
That is why you do not add another van.

ezért means therefore, so, or that is why.

It connects the two ideas:

• the bedroom window is closed
• because of that, the room stays warm in the morning

So the logic is:

Ablak zárva van → ezért a szoba meleg marad

The comma before ezért is normal, because it links two clauses.

Here reggel works as a time adverb meaning in the morning.

Hungarian often uses bare time words like this:

• reggel = in the morning
• este = in the evening
• holnap = tomorrow

So reggel here is not really the morning as a noun. It is an adverbial time expression.

If you said a reggel, that would be the morning as a noun, which is not what this sentence needs.

Because Hungarian word order is flexible and depends a lot on information structure.

In this sentence:

ezért reggel meleg marad a szoba

the flow is roughly:

• ezért = because of that
• reggel = in the morning
• meleg marad = stays warm
• a szoba = the room

This order highlights the result stays warm.

You could also say:

Ezért reggel a szoba meleg marad.

That is also grammatical, but the emphasis and rhythm are slightly different. Hungarian often moves elements around depending on what is being presented as the main point.

Formally, marad is present tense:

• marad = stays / remains

But Hungarian very often uses the present tense to talk about the future when the time is clear from context.

Here, reggel makes the time clear, so:

• reggel meleg marad a szoba

can naturally mean:

• the room stays warm in the morning
• or, in natural English, the room will stay warm in the morning

So the Hungarian form is present, but the meaning can easily be future-like.

Because a/az is the Hungarian definite article, like English the.

• a hálószoba ablaka = the bedroom window
• a szoba = the room

In the possessive phrase, the article normally goes at the beginning of the whole noun phrase:

• a hálószoba ablaka

not before both nouns separately.

Also, Hungarian keeps the article with a definite noun even if that noun comes later in the sentence, so a szoba still needs a even though it comes after meleg marad.