Putnica čeka u čekaonici dok ne čuje poruku na razglasu.

Putnica is the feminine singular form meaning female passenger or female traveller. It is in the nominative singular because it is the subject of the sentence.

If the passenger were male, you would usually say putnik.

Because u is followed by the locative when it means in a place, with no movement involved.

• base form: čekaonica = waiting room
• locative singular: čekaonici = in the waiting room

So:

• u čekaonici = in the waiting room
• u čekaonicu = into the waiting room

That second one uses the accusative because it shows movement toward a place.

Yes. This is completely normal in Croatian.

• čekati = to wait
• čekaonica = waiting room

So the sentence literally has the idea the passenger waits in the waiting room. That repetition is not strange in Croatian, even if English might sometimes avoid it stylistically.

Because poruku is the accusative singular form, used for the direct object of the verb čuje.

• nominative: poruka = message / announcement
• accusative: poruku = message / announcement as the thing being heard

Since the passenger hears the message, poruku is the correct form.

This is one of the most important things to notice in the sentence.

In Croatian, until is commonly expressed with dok ne + verb.

So:

• dok ne čuje = until she hears

The ne is required in this pattern, even though the overall meaning is positive in English. It does not mean she does not hear it. It means she waits up to the moment when she hears it.

A useful contrast is:

• dok čuje = while she hears / as long as she hears
• dok ne čuje = until she hears

Čuje is the 3rd person singular present form of čuti.

It matches the subject putnica, which is she.

So:

• ja čujem = I hear
• ti čuješ = you hear
• ona čuje = she hears

After time expressions like dok ne, Croatian often uses the present form for something that will happen later, just as English also says until she hears, not until she will hear.

Na razglasu means something like:

• over the loudspeaker
• on the PA system
• over the public address system

The noun is:

• razglas = loudspeaker system / PA system

And here it is in the locative singular:

• na razglasu

This is an idiomatic expression. The preposition na does not mean the message is physically sitting on top of something. It means the message is being broadcast through that system.

Because na can also take the locative when it indicates location or a medium/channel, not movement.

Here:

• base form: razglas
• locative singular: razglasu

So na razglasu is the normal form for on/over the PA system.

As with u, the case changes depending on meaning:

• na stolu = on the table
• na razglasu = on/over the PA system

Because Croatian has no articles.

So nouns like putnica, čekaonica, and poruka can mean a or the, depending on context.

That means:

• putnica can be a passenger or the passenger
• poruku can be a message or the message

The context or the larger situation tells you which one is meant.

No. By itself, dok often means while.

But dok ne usually means until.

Compare:

• Dok čeka, čita. = While she is waiting, she reads.
• Čeka dok ne čuje poruku. = She waits until she hears the message.

So the little word ne changes the meaning of the whole time clause.

Yes, Croatian word order is more flexible than English word order.

The sentence as given is neutral and natural:

• Putnica čeka u čekaonici dok ne čuje poruku na razglasu.

But other orders are possible if you want to emphasize something different, for example:

• U čekaonici putnica čeka dok ne čuje poruku na razglasu.
• Putnica u čekaonici čeka dok ne čuje poruku na razglasu.

The basic meaning stays the same, but the emphasis shifts slightly. The original version is a very normal default choice.