Czekaliśmy dwadzieścia dwie minuty, zanim projektor zaczął działać.

In Polish, the subject pronoun is often omitted because the verb ending already shows who is doing the action.

• czekaliśmy = we waited / we were waiting
• the ending -liśmy tells you it is 1st person plural: we

You could add my for emphasis, but it is not necessary:

• My czekaliśmy... = We were the ones waiting...

Without emphasis, leaving my out is the normal choice.

Czekaliśmy is the past tense of czekać for we. It is built from the past stem plus a personal ending.

It also shows grammatical gender of the group:

• czekaliśmy = used for a mixed group or a group of males
• czekałyśmy = used if the speakers are all female

So this sentence suggests the speakers were either mixed-gender or male.

It can mean either, depending on context.

Polish does not have a separate past continuous form like English was waiting / were waiting. Instead, Polish often uses the imperfective past to cover both ideas.

So czekaliśmy can correspond to:

• we waited
• we were waiting

In this sentence, because there is a clear time duration, English usually prefers we waited.

Because minuta is a feminine noun, and the 2 part of the number must agree with that.

• masculine/neuter: dwa
• feminine: dwie

So:

• dwie minuty = two minutes
• dwadzieścia dwie minuty = twenty-two minutes

This happens with numbers ending in 2, 3, 4 as well, except for the teens:

• 22 minuty
• 23 minuty
• 24 minuty
• but 12 minut, 13 minut, 14 minut

Here minuty is functioning as part of a time-duration expression, so it is in the accusative plural.

With many non-masculine-personal nouns, the accusative plural looks exactly like the nominative plural, so you see:

• minuty

In other words, the form looks simple, but its job in the sentence is accusative: it tells you how long the waiting lasted.

Because the sentence is telling you how long they waited, not directly what they waited for.

Polish uses:

• czekać na + accusative = to wait for
• a time expression without na = to wait for a certain amount of time

So:

• Czekaliśmy dwadzieścia dwie minuty = We waited for twenty-two minutes
• Czekaliśmy na projektor = We waited for the projector

If you wanted both ideas, you could say something like:

• Czekaliśmy dwadzieścia dwie minuty na projektor
• or more naturally in this context, Czekaliśmy dwadzieścia dwie minuty, aż projektor zacznie działać

Zanim introduces a subordinate clause and means before.

In this sentence, it connects the period of waiting with the later event:

• first: they waited
• then: the projector started working

So the structure is essentially:

• We waited twenty-two minutes before the projector started working.

A useful way to feel its meaning is:

• zanim = before the moment when

Because zanim introduces a subordinate clause, and in standard Polish such clauses are separated by a comma.

So:

• Czekaliśmy dwadzieścia dwie minuty, zanim projektor zaczął działać.

If the order is reversed, the comma is still used:

• Zanim projektor zaczął działać, czekaliśmy dwadzieścia dwie minuty.

Because zaczął działać means started working / began to function, while działał just means was working / worked.

The sentence focuses on the change of state:

• before: the projector was not functioning
• then: it began functioning

That is why Polish uses:

• zacząć + infinitive
• zaczął działać = started to work

If you said projektor działał, it would describe the projector as already working, not the moment when it began.

Because zaczął is perfective, and that fits a single completed event: the moment the projector started working.

• zaczął = he/it started
• zaczynał = he/it was starting / used to start

Here we want one specific event that ended the waiting, so zaczął is the natural choice.

This is a very common Polish pattern:

• ongoing/background action: often imperfective
• single completed event: often perfective

So:

• czekaliśmy = ongoing waiting
• zaczął działać = one completed starting event

Because projektor is a masculine singular noun, and the past tense agrees with it.

So:

• projektor zaczął = masculine singular
• if the noun were feminine, you would get zaczęła
• if it were neuter, you would get zaczęło

For example:

• drukarka zaczęła działać = the printer started working
• urządzenie zaczęło działać = the device started working

Yes. Polish word order is fairly flexible.

You can say:

• Czekaliśmy dwadzieścia dwie minuty, zanim projektor zaczął działać.
• Zanim projektor zaczął działać, czekaliśmy dwadzieścia dwie minuty.

Both are correct. The difference is mainly emphasis:

• the original version starts with the waiting
• the second version foregrounds the before the projector started working part

The original sentence sounds natural and neutral.

Because Polish has no articles. There is no direct equivalent of a or the in normal noun phrases.

So projektor can mean:

• a projector
• the projector

Context tells you which one is meant. In this sentence, the situation clearly points to the projector.