Po zamknięciu drzwi teściowa zapytała, czy wszyscy mają bilety i klucze.

Po zamknięciu drzwi means after closing the door / after the door was closed.

Literally:

• po = after
• zamknięciu = closing / the act of closing
• drzwi = door

So the structure is not a full clause like after she closed the door, but a noun-based phrase: after the closing of the door.

This kind of structure is very common in Polish and often sounds natural and compact.

Because po usually requires the locative case, and zamknięcie changes in the locative to zamknięciu.

So:

• zamknięcie = nominative / dictionary form
• po zamknięciu = locative after po

This is a very common pattern:

• po obiedzie = after dinner
• po spotkaniu = after the meeting
• po zamknięciu = after closing

Drzwi is one of those Polish nouns that is plural in form, even when it refers to a single door. English learners often notice this quickly because it feels unusual.

So:

• drzwi = door
• grammatically, it behaves like a plural noun

That is why you often see plural-looking agreement around it in other contexts.

In po zamknięciu drzwi, drzwi stays drzwi, because this is also the genitive form here.

Teściowa means mother-in-law.

More specifically, it is the feminine noun for a female in-law of that type:

• teściowa = mother-in-law
• teść = father-in-law

So the sentence tells us that the speaker is talking about a woman, and that matters for the verb form too.

Because teściowa is feminine, and Polish past tense agrees with the gender of the subject.

So:

• zapytał = he asked
• zapytała = she asked

Since teściowa is a woman, the correct form is zapytała.

This is about aspect, which is very important in Polish verbs.

• zapytała is from zapytać and is perfective
• pytała is from pytać and is imperfective

In this sentence, zapytała means she asked once, as a completed action.

So:

• teściowa zapytała = the mother-in-law asked
• teściowa pytała would suggest she was asking, used to ask, or was in the process of asking, depending on context

Here, the completed one-time action fits best.

Czy introduces an indirect yes/no question.

In this sentence:

• teściowa zapytała = the mother-in-law asked
• czy wszyscy mają bilety i klucze = whether everyone has tickets and keys

So czy here means whether / if.

Compare:

• Czy masz bilet? = Do you have a ticket?
• Zapytała, czy masz bilet. = She asked whether / if you have a ticket.

So English often uses if or whether, while Polish uses czy.

This is a very natural question, because English everyone is grammatically singular, but Polish often expresses this idea differently.

Wszyscy literally means all (people), so it is plural:

• wszyscy = everyone / everybody / all of them
• mają = they have

So Polish is thinking more like:

• whether all of them have tickets and keys

If you wanted a singular idea, you might use każdy:

• czy każdy ma bilet = whether each person has a ticket

But wszyscy mają is completely normal and very common.

Because Polish often keeps the subordinate clause in the present tense when it refers to a situation that is current from the point of view of the question being asked.

So:

• teściowa zapytała = the mother-in-law asked
• czy wszyscy mają bilety i klucze = whether everyone has tickets and keys

English can also do this:

• She asked if everyone had tickets and keys but Polish does not have to shift the tense in the same way English often does.

So the Polish sentence is perfectly natural.

They are the direct objects of mają (have), so they are in the accusative plural.

However, for many inanimate masculine nouns, the accusative plural looks exactly like the nominative plural.

So:

• bilety = tickets
• klucze = keys

Here those forms serve as the objects of mają:

• mają bilety i klucze = they have tickets and keys

That is why the forms look simple and unchanged.

Yes, Polish word order is fairly flexible, although some orders sound more natural than others.

The given sentence:

• Po zamknięciu drzwi teściowa zapytała, czy wszyscy mają bilety i klucze.

is neutral and natural.

You could change the order for emphasis, for example:

• Teściowa zapytała po zamknięciu drzwi, czy wszyscy mają bilety i klucze.

This still works, but it may slightly shift the focus.

In general, the original version sounds like a normal narrative sentence: first the door is closed, then the mother-in-law asks the question.

In theory, drzwi can refer to a door as a grammatical plural noun, and in some contexts it can also be understood more generally as doors. But in a sentence like this, the most natural reading is simply the door.

So:

• po zamknięciu drzwi = after closing the door

The exact number is usually understood from context, and in everyday translation English normally uses singular door here.

Because Polish does not have articles like the or a/an.

So:

• drzwi can mean door / the door
• teściowa can mean mother-in-law / the mother-in-law
• bilety can mean tickets / the tickets

The exact meaning is understood from context.

In this sentence, English naturally uses the mother-in-law, the door, and possibly tickets and keys, but Polish does not need separate article words to express that.