Otwórz proszę furtkę, bo dzieci są na podwórku.

Otwórz is the imperative form, meaning open!

• otworzyć = to open (dictionary form / infinitive)
• otwórz = open! (said to one person)

It comes from the perfective verb otworzyć, which is used when you mean a completed action: open it.

So Otwórz proszę furtkę means Please open the gate, not just to open the gate.

Because it is the direct object of the verb open, so it takes the accusative case.

• nominative: furtka
• accusative: furtkę

This is very common with feminine nouns ending in -a:

• książka → książkę
• herbata → herbatę
• furtka → furtkę

So:

• furtka = the gate / a gate as the subject
• otwórz furtkę = open the gate as the object

Furtka usually means a small gate, especially a pedestrian gate in a fence.

It is not the same as:

• drzwi = door
• brama = large gate
• furtka = small gate / garden gate / side gate

So in this sentence, it suggests a gate leading into a yard or enclosed area, not a house door.

Here proszę makes the command more polite. In this sentence it works like please.

So:

• Otwórz furtkę. = Open the gate.
• Otwórz proszę furtkę. = Please open the gate.

A useful point: proszę can mean different things in different contexts, such as:

• please
• here you are
• I’m asking
• go ahead

But in this sentence, it simply softens the imperative.

Yes. Polish word order is flexible, and proszę can appear in different positions.

All of these are natural:

• Otwórz proszę furtkę.
• Proszę, otwórz furtkę.
• Otwórz furtkę, proszę.

They all mean roughly the same thing, though the tone may shift slightly:

• Proszę, otwórz furtkę. can sound a bit more directly like Please, open the gate.
• Otwórz furtkę, proszę. often sounds especially natural in everyday speech.

Because dzieci is the plural form meaning children.

• singular: dziecko = child
• plural: dzieci = children

And because the subject is plural, the verb must also be plural:

• dziecko jest = the child is
• dzieci są = the children are

So dzieci są na podwórku means the children are in/on the yard.

Because Polish uses certain prepositions idiomatically, and with podwórko the natural expression is na podwórku.

Even though English says in the yard, Polish says literally on the yard/courtyard:

• na podwórku = in the yard / in the courtyard

This is just how Polish expresses location with this noun. Many place expressions have to be learned as fixed patterns.

Because after na when it means location, Polish uses the locative case.

• nominative: podwórko
• locative: na podwórku

So:

• podwórko = yard
• na podwórku = in the yard

This use of na + locative is very common for places:

• na stole = on the table
• na ulicy = on the street
• na podwórku = in the yard

Bo means because.

In this sentence:

• Otwórz proszę furtkę, bo dzieci są na podwórku.
• Please open the gate, because the children are in the yard.

Bo is very common in everyday spoken and written Polish. It is neutral and natural.

A slightly more formal alternative is:

• ponieważ = because / since

So:

• bo dzieci są na podwórku = everyday, very natural
• ponieważ dzieci są na podwórku = a bit more formal

Because the speaker wants one completed action: open the gate.

In Polish, imperatives often reflect aspect:

• otwierać = imperfective, opening in general / repeatedly / process
• otworzyć = perfective, open completely / do it once

So otwórz suggests:

• do it now
• do it once
• achieve the result that the gate is open

This is exactly what you would normally want in a sentence like this.

Not exactly.

• Otwórz furtkę = Open the gate as a completed action
• Otwieraj furtkę = more like Be opening the gate / Open the gate repeatedly / Start opening it, depending on context

In many situations, otwieraj would sound less natural here unless the speaker is focusing on the process or repeating the instruction. For a simple one-time request, otwórz is the normal choice.

It can change, because Polish word order is fairly flexible. The original sentence is natural, but other versions are possible.

For example:

• Otwórz proszę furtkę, bo dzieci są na podwórku.
• Otwórz furtkę, proszę, bo dzieci są na podwórku.
• Bo dzieci są na podwórku, otwórz proszę furtkę.

The most neutral everyday version is probably the original one. Changing the order usually affects emphasis more than core meaning.

A few useful pronunciation points:

• otwórz: the ó sounds like u
• proszę: the final ę is often pronounced less strongly in normal speech, especially at the end of a word
• furtkę: the tk cluster is pronounced clearly
• dzieci: starts with a sound like jyeh
  • chee, not like English dee-eh-tee-see
• podwórku: again, ó = u
• rz in otwórz sounds like ż

So two important spelling facts are:

• ó is pronounced like u
• rz is pronounced like ż

Even though the spelling looks complicated, the sentence is very normal in spoken Polish.