Es curioso que hoy nadie haya hablado del examen.

Because es curioso que expresses a reaction, judgement, or evaluation. In Spanish, that kind of expression normally triggers the subjunctive in the clause that follows.

So the structure is:

• Es curioso que + subjunctive

Other similar examples are:

• Es extraño que no venga.
• Es bueno que lo sepas.
• Es raro que estén aquí.

The speaker is not just stating a fact; they are commenting on it, and that is why the subjunctive appears.

Because haya hablado is the present perfect subjunctive, and it refers to something that has already happened, or in this case, something that has not happened up to now.

Compare:

• Es curioso que nadie hable del examen.
  = It is strange that nobody talks / is talking about the exam.
  This sounds more general or more about the present situation.

• Es curioso que nadie haya hablado del examen.
  = It is strange that nobody has talked about the exam.
  This focuses on the fact that, up to now, no one has done it.

So haya hablado is used because the sentence is about a completed action within the time frame of today.

Because ha hablado is indicative, and after es curioso que Spanish wants the subjunctive, not the indicative.

So:

• nadie ha hablado = nobody has talked
• nadie haya hablado = that nobody has talked

In this sentence, the second clause depends on es curioso que, so the mood changes.

A good way to think about it is:

• Ha hablado = plain statement of fact
• Haya hablado = fact seen through the speaker’s reaction or judgement

Hoy helps explain why the perfect form is so natural, especially in Spain.

In Peninsular Spanish, the present perfect is very commonly used for actions in a time period that is still considered open, such as:

• hoy
• esta mañana
• esta semana
• este año

So hoy nadie haya hablado fits the idea of up to this point today.

In Spain, this sounds very natural. In many parts of Latin America, speakers often prefer forms closer to the preterite in equivalent contexts, but for Spain, the sentence given is exactly what you would expect.

Because nadie itself already carries the negative meaning, and here it is placed before the verb.

When negative words like nadie, nunca, nada, or ninguno come before the verb, Spanish does not add no.

So:

• Nadie ha hablado. = Nobody has spoken.

But if the negative word comes after the verb, then Spanish does use no:

• No ha hablado nadie. = Nobody has spoken.

Both are correct, but the structure changes.

In your sentence, nadie is the subject before the verb, so no extra no is needed.

Because del is the contraction of de + el.

So:

• de + el = del

This contraction is normally required in Spanish:

• hablar del examen
• venir del trabajo
• salir del coche

The only common exception is when El is part of a proper name, such as:

• de El Escorial

Here, though, el examen is just a normal noun phrase, so del is required.

Because hablar de is the normal way to say to talk about something.

So:

• hablar de política
• hablar de un problema
• hablar del examen

You can also hear alternatives like:

• hablar sobre el examen
• hablar acerca del examen

But hablar de is the most common and neutral choice in everyday Spanish.

Yes. Es curioso que hoy nadie haya hablado sobre el examen is grammatically possible.

But there is a small difference in feel:

• hablar de = the most common, natural, everyday way to say talk about
• hablar sobre = also correct, sometimes slightly more formal or more explicitly on the subject of
• hablar acerca de = correct, often a bit more formal

So del examen is probably the most natural choice in ordinary conversation.

Yes. After es curioso, you need que to introduce the subordinate clause.

The pattern is:

• Es curioso que + clause

So:

• Es curioso que hoy nadie haya hablado del examen.

Without que, the sentence would not work grammatically in the same way.

Yes, a little. Spanish allows some flexibility, and changing the order can shift the focus slightly.

For example:

• Es curioso que hoy nadie haya hablado del examen.
• Es curioso que nadie haya hablado del examen hoy.
• Es curioso que nadie haya hablado hoy del examen.

All of these are possible, but the emphasis changes a bit:

• hoy near the start highlights today
• hoy near the end can sound like an afterthought or final time reference
• del examen near the end gives the topic a little extra weight

The original sentence is very natural and clearly foregrounds today.

Normally, no, not in this context.

hablara is the imperfect subjunctive, and it does not fit well with a present main clause like es curioso when you are talking about something that has not happened up to now today.

For this sentence, the natural choice is:

• Es curioso que hoy nadie haya hablado del examen.

If the main clause were in the past, then Spanish might use a past subjunctive form, for example:

• Era curioso que nadie hubiera hablado del examen.

So hablara is not the right form for the meaning and time reference of the original sentence.