La professora diu que, si avui suspenem, demà hi haurà un altre examen.

La professora means the teacher and is feminine singular.

• la = the (feminine singular)
• professora = female teacher

Catalan nouns and articles have gender, so professora takes la. If it were a male teacher, it would be El professor.

diu means says, and que means that.

So La professora diu que... is literally The teacher says that...

In English, that is often optional:

• The teacher says that...
• The teacher says...

In Catalan, que is normally kept after verbs like dir (to say), pensar (to think), creure (to believe), etc.

diu is the 3rd person singular present indicative of dir:

• jo dic = I say
• tu dius = you say
• ell/ella diu = he/she says

Here it matches la professora, which is singular: the teacher says.

That part is an inserted conditional clause: if we fail today.

The sentence is structured like this:

La professora diu que, si avui suspenem, demà hi haurà un altre examen.

The commas help mark off the inserted if clause in the middle of the sentence.

You could think of the main structure as:

• La professora diu que demà hi haurà un altre examen and then the condition is inserted:
• si avui suspenem

This punctuation is very natural in Catalan.

Yes. In this sentence, si means if.

So:

• si avui suspenem = if we fail today

Catalan si can also mean whether in other contexts, but here the meaning is clearly conditional: if.

suspenem is the 1st person plural present indicative of suspendre.

• suspenem = we fail

Here it refers to failing an exam or test.

The subject is understood from the verb ending, so Catalan does not need to say nosaltres:

• suspenem already means we fail

Because Catalan normally uses the present indicative after si for a real future condition.

So Catalan says:

• si avui suspenem, demà hi haurà...

Literally:

• if today we fail, tomorrow there will be...

This is similar to English:

• If we fail today, there will be another exam tomorrow.

You do not normally use the future after si in this kind of sentence.

avui means today, and it is an adverb of time.

Catalan word order is fairly flexible, so avui can often move around. Here, si avui suspenem is a natural way to say if we fail today.

Putting avui before the verb gives the time reference early:

• si avui suspenem = if today we fail

You might also hear other word orders in some contexts, but this one is completely normal.

hi haurà means there will be.

It comes from the existential expression haver-hi, which is used to mean there is / there are / there will be.

So:

• hi ha = there is / there are
• hi haurà = there will be

The hi is an essential part of this expression. You generally do not leave it out.

So:

• demà hi haurà un altre examen = tomorrow there will be another exam

Although haver is historically related to have, in haver-hi it does not mean possession. It is the standard way to express existence:

• hi ha un llibre = there is a book
• hi haurà un examen = there will be an exam

So in this sentence, hi haurà is not about someone having an exam. It means that an exam will exist / take place.

un altre examen means another exam.

• un = a / one
• altre = other / another
• examen = exam

Together, un altre is the normal way to say another in this context: one more exam.

If you only said altre examen, it would sound less natural here. un altre examen is the expected phrasing.

examen is masculine, so it takes un:

• un examen = an exam

That is why the sentence has:

• un altre examen

Its plural is exàmens.

Yes. demà means tomorrow, and Catalan allows some flexibility with adverbs.

In this sentence:

• demà hi haurà un altre examen

That is very natural. But depending on style or emphasis, demà could sometimes appear elsewhere.

Still, the version in your sentence is probably the most straightforward and idiomatic.

No. Catalan often drops subject pronouns when the verb ending already makes the subject clear.

• suspenem already tells you the subject is we

So si avui suspenem naturally means if we fail today, without needing nosaltres.

If nosaltres were added, it would usually be for emphasis:

• si nosaltres avui suspenem...

But in ordinary speech, that is unnecessary.