Przed koncertem dzieci zostawiły instrumenty za kurtyną, żeby na scenie było więcej miejsca.

Because the preposition przed requires the instrumental case when it means before (in time) or in front of (in space, when there is no movement toward it).

So:

• koncert = nominative/dictionary form
• koncertem = instrumental

That is why before the concert becomes przed koncertem.

It can mean both.

In this sentence, przed koncertem means before the concert in a time sense.

But przed can also be spatial:

• Stoję przed teatrem. = I am standing in front of the theatre.

So English speakers need to learn that one Polish preposition can cover both before and in front of, depending on context.

Because dzieci takes non-masculine-personal plural agreement in standard Polish, so the past tense form is -ły, not -li.

That is why you say:

• dzieci przyszły
• dzieci zrobiły
• dzieci zostawiły

Even though children are people, dzieci behaves grammatically this way. For a learner, the safest rule is: with dzieci, use forms like były, zrobiły, poszły, zostawiły.

Zostawiły is the past tense plural form of zostawić, which usually means:

• to leave
• to leave behind
• to put somewhere and go away
• sometimes to abandon

In this sentence it means the children left the instruments somewhere.

The verb zostawić is perfective, so it presents the action as completed: they placed the instruments there, and that action was done.

Its imperfective partner is zostawiać.

Because here instrumenty is the accusative plural, and for many masculine inanimate nouns, the accusative plural looks exactly like the nominative plural.

So:

• nominative plural: instrumenty
• accusative plural: instrumenty

Since zostawić takes a direct object, instrumenty is in the accusative.

Polish normally has no articles, so there is no separate word for the or a/an.

Also, Polish often leaves out possessive words like their, his, her, when the meaning is obvious from context. In this sentence, it is natural to understand that the children left their instruments.

If you wanted to make that explicit, you could say:

• dzieci zostawiły swoje instrumenty

But the version without swoje sounds very normal.

Because za can take different cases depending on meaning.

• za + instrumental = location, behind
• za + accusative = movement to behind

Here the instruments are located behind the curtain, so Polish uses the instrumental:

• za kurtyną = behind the curtain

Compare:

• Położyli instrumenty za kurtynę. = They put the instruments behind the curtain.
  (movement to that place)
• Instrumenty były za kurtyną. = The instruments were behind the curtain.
  (location)

In your sentence, the final location is what matters.

Because after za in a location meaning, Polish uses the instrumental.

The noun is:

• kurtyna = curtain
• kurtyną = instrumental singular

So za kurtyną is a very standard preposition + case combination.

Żeby introduces a clause of purpose or intended result. Here it means:

• so that
• in order that

So:

• ...zostawiły instrumenty za kurtyną, żeby na scenie było więcej miejsca.
• ...left the instruments behind the curtain so that there would be more space on the stage.

A slightly more formal alternative is aby:

• ..., aby na scenie było więcej miejsca.

But żeby is very common and natural in everyday Polish.

Because na also changes case depending on whether you mean location or movement.

• na + locative = on / at (location)
• na + accusative = onto / to (movement toward)

Here the sentence means on the stage as a location, so it uses the locative:

• scena = stage
• na scenie = on the stage

Compare:

• Weszli na scenę. = They went onto the stage.
• Byli na scenie. = They were on the stage.

Because this is an impersonal/existential type of construction: żeby było więcej miejsca means something like so that there would be more space.

In Polish, expressions like this often use 3rd person singular neuter:

• było
• jest
• będzie

So the verb is not really agreeing with dzieci or with a normal plural subject here. It is functioning like English there was / there would be.

That is why było is correct.

Because after words of quantity or comparison like więcej (more), Polish usually puts the noun in the genitive.

So:

• miejsce = place, space
• miejsca = genitive singular

That gives:

• więcej miejsca = more space

You see the same pattern in many other expressions:

• dużo czasu = a lot of time
• mało pieniędzy = little money
• więcej wody = more water

Yes. In standard Polish spelling, a subordinate clause introduced by żeby is separated with a comma.

So:

• Przed koncertem dzieci zostawiły instrumenty za kurtyną, żeby na scenie było więcej miejsca.

That comma is required in normal written Polish.

Yes, Polish word order is relatively flexible, although some versions sound more natural than others.

The given sentence is very neutral:

• Przed koncertem dzieci zostawiły instrumenty za kurtyną, żeby na scenie było więcej miejsca.

You could also move parts around for emphasis, for example:

• Dzieci zostawiły instrumenty za kurtyną przed koncertem, żeby na scenie było więcej miejsca.
• Żeby na scenie było więcej miejsca, dzieci zostawiły instrumenty za kurtyną przed koncertem.

The meaning stays similar, but the emphasis changes. The original version sounds smooth and natural because it starts with the time phrase przed koncertem and ends with the purpose clause.