Gdy usłyszeliśmy alarm drugi raz, zaczęliśmy schodzić po schodach szybciej niż wcześniej.

Here gdy means when.

In this sentence, gdy usłyszeliśmy alarm drugi raz = when we heard the alarm a second time.

For many everyday purposes, gdy and kiedy can both mean when. In a sentence like this, they are often interchangeable:

• Gdy usłyszeliśmy alarm...
• Kiedy usłyszeliśmy alarm...

A small nuance is that gdy can sound a little more written or narrative, while kiedy is often more common in speech.

Because Gdy usłyszeliśmy alarm drugi raz is a subordinate clause introduced by gdy.

Polish normally separates this kind of clause with a comma:

• Gdy usłyszeliśmy alarm drugi raz, zaczęliśmy...

This is similar to English When we heard the alarm a second time, we began...

Polish often leaves out subject pronouns when the verb ending already shows who the subject is.

Here:

• usłyszeliśmy = we heard
• zaczęliśmy = we began

The ending -liśmy tells you the subject is we, so my is unnecessary unless you want emphasis.

Compare:

• Usłyszeliśmy alarm. = We heard the alarm.
• My usłyszeliśmy alarm. = We heard the alarm (with extra emphasis on we)

Usłyszeliśmy is the past tense of the perfective verb usłyszeć, meaning to hear in the sense of to catch a sound / to hear something happen.

So:

• usłyszeliśmy alarm = we heard the alarm

By contrast, słyszeliśmy comes from słyszeć, which is imperfective. It often means we were hearing, we used to hear, or simply focuses less on the completed event.

In this sentence, the point is that the alarm was heard as a specific event, so the perfective usłyszeliśmy fits better.

It comes from:

• infinitive: usłyszeć
• past stem: usłysz-
• masculine-personal plural past ending: -eliśmy

So:

• usłyszeliśmy = we heard

This -liśmy ending is very common for we in the past tense:

• zrobiliśmy = we did
• poszliśmy = we went
• zaczęliśmy = we began

Because alarm is the direct object of usłyszeliśmy, so it is in the accusative case.

For many masculine inanimate nouns, the accusative singular looks exactly like the nominative singular. So:

• nominative: alarm
• accusative: alarm

That is why you see:

• usłyszeliśmy alarm

not because there is no case, but because the accusative form happens to be identical here.

Yes. Drugi raz literally means second time or a second time.

So:

• usłyszeliśmy alarm drugi raz = we heard the alarm a second time

This is a very common Polish way to express repetition.

Another common expression is:

• po raz drugi = for the second time

So these are both possible:

• usłyszeliśmy alarm drugi raz
• usłyszeliśmy alarm po raz drugi

They are very close in meaning.

Yes, Polish word order is fairly flexible, though some placements sound more natural than others.

You could say:

• Gdy drugi raz usłyszeliśmy alarm, ...
• Gdy usłyszeliśmy drugi raz alarm, ...
• Gdy usłyszeliśmy alarm drugi raz, ...

The original version is natural and clear. Moving drugi raz changes emphasis slightly, but not the core meaning.

Because zaczęliśmy schodzić means we started to go down / we began going down, while zeszliśmy would mean we went down / we came down as a completed action.

So the sentence focuses on the start of the action:

• zaczęliśmy schodzić = we began descending

This is different from simply saying the whole descent happened.

Because after zacząć (to begin/start), Polish very often uses an infinitive describing an action in progress, and the imperfective verb is usually the natural choice.

• zaczęliśmy schodzić = we began going down

The imperfective schodzić presents the action as ongoing or unfolding. That fits the idea of beginning an action.

They are an aspect pair:

• schodzić = imperfective
• zejść = perfective

Very roughly:

• schodzić focuses on the process: to be going down / to go down
• zejść focuses on completion: to go down and finish doing so

In this sentence, schodzić is used because the sentence is about starting the action, not completing it.

Po schodach is the normal expression for movement on/along the stairs, especially when going up or down them.

So:

• schodzić po schodach = to go down the stairs
• wchodzić po schodach = to go up the stairs

Even though po often means after or on, with stairs it is just part of the standard phrase.

It is in the locative plural.

The preposition po often takes the locative, and schody is a plural noun:

• nominative plural: schody
• locative plural: schodach

So:

• po schodach = on/along the stairs

Because szybciej is the comparative form of the adverb szybko (quickly).

Forms:

• szybko = quickly
• szybciej = more quickly / faster
• najszybciej = most quickly / fastest

Since the sentence compares the speed of descending now with the speed earlier, the comparative adverb is needed:

• schodzić szybciej = to go down faster

Because niż means than in comparisons.

So:

• szybciej niż wcześniej = faster than earlier

This is a standard comparative structure:

• wolniej niż zwykle = more slowly than usual
• lepiej niż przedtem = better than before
• szybciej niż wcześniej = faster than earlier

Here wcześniej means earlier or previously.

So:

• szybciej niż wcześniej = faster than earlier / faster than before

It is an adverb, not an adjective. It refers to the earlier situation or earlier speed, not directly to a noun.

Yes, in many contexts it could.

For example:

• szybciej niż wcześniej
• szybciej niż przedtem

Both can mean faster than before.
Wcześniej is often a bit more neutral and very common. Przedtem also works well and can sound slightly more like before that.

Because both actions are narrated as past events:

• usłyszeliśmy = we heard
• zaczęliśmy = we began

The infinitive schodzić does not show tense by itself; the tense comes from zaczęliśmy. So:

• zaczęliśmy schodzić = we began to go down

It has two parts:

1. Gdy usłyszeliśmy alarm drugi raz
   = a time clause: When we heard the alarm a second time

2. zaczęliśmy schodzić po schodach szybciej niż wcześniej
   = the main clause: we began going down the stairs faster than before

So the structure is:

• When X happened, Y happened.

This is a very common Polish sentence pattern.