Learn Hardcore Croatian: Tijekom predavanja studenti postavljaju pitanja o tome kako svemirska postaja radi i kako tamo žive ljudi. - During the lecture the students ask questions about how the space station works and how people live there.

tijekom predavanja – during the lecture, focuses on time (while the lecture is going on)
na predavanju – at the lecture, focuses on place/situation (at that event)

Your sentence:

Tijekom predavanja studenti postavljaju pitanja…
= While the lecture is in progress, they ask questions.

If you said:

Na predavanju studenti postavljaju pitanja…
= At the lecture, they ask questions (they tend to ask questions in that setting).

Often they overlap in meaning and both sound natural here.

Why is it studenti and not studenti su or something with a verb “to be”?

In this sentence studenti is the subject, and the main verb is already there: postavljaju.

Word-by-word:

studenti – the students (nominative plural)
postavljaju – ask / are asking (3rd person plural, present)
pitanja – questions (direct object)

Croatian doesn’t need an extra “to be” verb here.
It’s not like English “The students are asking questions” with are + asking.
The single verb postavljaju already includes:

person: they
number: plural
tense: present

What is the difference between postavljaju pitanja and pitaju?

Both relate to asking, but they’re used a bit differently:

pitati – to ask (usually someone a question or about something)
- Studenti pitaju profesora. – The students ask the professor.
- Studenti pitaju kako svemirska postaja radi.
postavljati pitanje / pitanja – literally “to set/pose a question/questions”
- This is the most standard, neutral way to say “ask questions” in a formal or careful style.
- postavljaju pitanja implies they are actually formulating and posing specific questions.

In your sentence, postavljaju pitanja sounds natural and a bit more formal/explicit than just pitaju.

Why is it pitanja (plural) and not pitanje (singular)?

Because the sentence describes students asking questions in general, not just one question.

pitanje – question (singular)
pitanja – questions (plural, nominative/accusative)

So:

postavljaju pitanje – they ask a question (one)
postavljaju pitanja – they ask questions (more than one, or in general)

Here pitanja is in the accusative plural (direct object of postavljaju).

What does the structure o tome kako… mean, and why do we need tome?

O tome kako… literally means about that, how…, and is a very common way to introduce an indirect question or explanation.

Breakdown:

o – about (preposition that takes the locative)
to – that / it (neuter pronoun)
tome – locative singular of to (used after o)
kako – how

So:

pitanja o tome kako svemirska postaja radi
= questions about how the space station works

In Croatian you usually say:

o tome kako…
o tome zašto…
o tome što…

You cannot just say pitanja o kako… – the tome is needed to connect o with the following kako-clause.

Which case is tome, and why is that case used here?

Tome is the locative singular of the pronoun to (that/it).

The preposition o (about) always takes the locative case:

o + knjiga → o knjizi
o + grad → o gradu
o + to → o tome

So, grammatically, o tome = “about that”, and then kako… specifies what “that” is (how something works, how people live, etc.).

Could we leave out tome and just say pitanja kako svemirska postaja radi?

You can say something like:

pitanja kako svemirska postaja radi

but it sounds a bit less natural and a bit more “direct”.
For the meaning “questions about how …”, Croatians very often prefer:

pitanja o tome kako svemirska postaja radi

The pattern pitanja o tome + kako/zašto/što… is very common and idiomatic, especially in neutral or formal style. Leaving out o tome can sound slightly incomplete or informal in this context.

Why isn’t there a comma before i kako tamo žive ljudi?

The sentence has two similar subordinate clauses joined by i (and):

kako svemirska postaja radi
(i) kako tamo žive ljudi

They both depend on pitanja o tome. In Croatian, when two clauses of the same type are joined with i, you often don’t put a comma before i, especially in a relatively short, simple sentence.

So this is normal:

…pitanja o tome kako svemirska postaja radi i kako tamo žive ljudi.

You could add a comma for extra clarity in writing, but it’s not required and most native speakers wouldn’t put one here.

Why is it kako svemirska postaja radi and not kako radi svemirska postaja?

Both orders are grammatically possible:

kako svemirska postaja radi
kako radi svemirska postaja

Differences:

kako svemirska postaja radi – more neutral word order (subject before verb)
kako radi svemirska postaja – slightly more emphasis on radi (the action of working/operating), or on the whole phrase as a question.

In indirect questions like this, the first version (kako svemirska postaja radi) is more common and feels more neutral/natural.

What exactly does radi mean here?

Radi is the 3rd person singular present of raditi (to work). In this context it means:

how the space station works / operates / functions

So:

svemirska postaja radi – the space station works (is functioning)
kako svemirska postaja radi – how the space station works / how it operates

It does not mean “works” as in “has a job”; it’s about functioning, operating.

Is svemirska postaja the only way to say “space station”? What about svemirska stanica?

Both are used:

svemirska postaja – space station
svemirska stanica – also space station

They are practically synonyms. Usage can vary by region and by speaker, but both are understandable and correct in standard Croatian. Your sentence is completely natural with svemirska postaja.

What does tamo add in kako tamo žive ljudi? Could we omit it?

Tamo means there, and it tells you where the people live (on/at the space station).

kako tamo žive ljudi – how people live there (on the station)

If the context is very clear (you’ve just been talking about the space station), you could omit tamo:

kako žive ljudi – how people live

But then it’s more general: “how people live (in general / under those conditions)”.
Adding tamo explicitly ties it to that place mentioned earlier (the space station).

Why is it kako tamo žive ljudi and not kako ljudi tamo žive? Is that also possible?

Both are possible and correct:

kako tamo žive ljudi
kako ljudi tamo žive

They mean the same: how people live there.

Word-order nuance (very slight):

kako tamo žive ljudi – a bit more neutral, the focus comes last on ljudi (people).
kako ljudi tamo žive – can put a tiny bit more focus on ljudi (the people) first.

In everyday speech you’ll hear both orders. Croatian allows flexible word order, especially in subordinate clauses like this.