Miután a barátnőm süteményt süt, a konyha meleg marad.

Miután means after and introduces a subordinate clause.

So in:

Miután a barátnőm süteményt süt, a konyha meleg marad.

the first part sets the time frame: After my girlfriend bakes pastries / a cake...

A few useful points:

• miután is a conjunction, not a noun or postposition
• it is followed by a full clause with its own subject and verb
• when this miután clause comes first, Hungarian normally uses a comma before the main clause

Because the sentence begins with a subordinate clause:

Miután a barátnőm süteményt süt,
a konyha meleg marad.

Hungarian uses a comma to separate the subordinate clause from the main clause, just like English often does with clauses such as after, when, because, etc.

Because Hungarian usually shows possession with a suffix on the noun.

• barátnő = girlfriend / female friend
• barátnőm = my girlfriend / my female friend

The -m ending means my.

You can also say az én barátnőm, but that is more emphatic, like my girlfriend in contrast to someone else’s. In neutral sentences, barátnőm is enough.

Not always. Barátnő can mean either:

• girlfriend
• female friend

So barátnőm can mean my girlfriend or my female friend. Context decides which one is meant. In many everyday contexts, people understand girlfriend, but the word itself is not strictly limited to romantic meaning.

Because it is the direct object of the verb süt (to bake), so it takes the accusative ending -t.

• sütemény = cake, pastry, baked treat
• süteményt = cake/pastry as the thing being baked

This is very common in Hungarian: direct objects usually get -t.

Examples:

• olvasok egy könyvet = I’m reading a book
• látok egy kutyát = I see a dog
• süteményt süt = she bakes pastry / a cake

This is about Hungarian’s indefinite and definite verb conjugation.

Here the object is süteményt, which is indefinite in meaning: a cake / some pastry / pastries rather than the cake. So Hungarian uses the indefinite verb form:

• süt = bakes

If the object were definite, you would use the definite conjugation:

• A süteményt süti. = She is baking the cake/pastry.

So:

• süteményt süt = bakes cake/pastry
• a süteményt süti = bakes the cake/pastry

Because that is a very normal Hungarian word order, especially with a bare indefinite object.

süteményt süt is a natural unit, roughly like bakes pastry / bakes cakes.

Hungarian word order is not fixed the way English word order is. It often depends on information structure and what is being emphasized. In a neutral sentence, an indefinite direct object often appears right before the verb.

So:

• A barátnőm süteményt süt. = neutral, natural
• A barátnőm süt süteményt. = possible, but more marked or different in rhythm/focus

Because a konyha is the subject here:

• a konyha = the kitchen
• meleg marad = stays warm

So the sentence literally says:

the kitchen stays warm

If you said a konyhában, that would mean in the kitchen, which is a location, not the subject.

Compare:

• A konyha meleg marad. = The kitchen stays warm.
• A konyhában meleg marad. = It stays warm in the kitchen.
  (Now the subject is not the kitchen itself.)

Literally, it means remains warm or stays warm.

• meleg = warm
• marad = remains, stays

Hungarian often uses an adjective plus marad to express that something continues in a state:

• nyitva marad = stays open
• csendes marad = stays quiet
• meleg marad = stays warm

So this part is very natural Hungarian.

Yes. In this form, the sentence most naturally sounds like a general/habitual statement:

Whenever/after my girlfriend bakes pastries, the kitchen stays warm.

Hungarian can use present tense for repeated or general situations. If you want to describe one completed event in the past, you would normally use past tense in both clauses:

Miután a barátnőm süteményt sütött, a konyha meleg maradt.

That means:

After my girlfriend baked pastries / a cake, the kitchen stayed warm.

So the present-tense version is best understood as a general pattern, not just one single past event.

It is understandable and grammatical, but the exact feel depends on context.

With present tense, miután can sound a bit formal or sequence-focused. If you mean a general repeated situation, some speakers might prefer amikor in everyday speech:

Amikor a barátnőm süteményt süt, a konyha meleg marad.

That sounds more like:

When/whenever my girlfriend bakes pastries, the kitchen stays warm.

So the original sentence is fine, but for a repeated habitual idea, amikor may sound more natural to some speakers.