Learn Hardcore Spanish (Spain): Para ese viaje, tenemos que reservar las habitaciones del hotel pronto. - For that trip, we have to book the hotel rooms soon.

Para ese viaje ≈ for that trip (with that trip as the purpose).
Por ese viaje would usually mean because of that trip or for that trip in the sense of in exchange for / on account of that trip, which sounds wrong here.

So in this context, para is the standard choice to introduce what something is intended for.

Could we also say para el viaje instead of para ese viaje? What is the difference?

Yes, para el viaje is also possible and correct. The difference is in how specific you are:

para ese viaje = for that trip (we both know which one: that particular one)
para el viaje = for the trip, still specific, but it sounds a bit more neutral or general, as if there is only one trip in mind or it has just been mentioned.

If, for example, people have been discussing several trips, ese viaje clearly singles out one of them. If there is only one obvious trip in the conversation, ese viaje and el viaje are both natural.

Why is ese viaje used instead of este viaje or aquel viaje?

Spanish makes a three-way distinction with este / ese / aquel:

este viaje: this trip, close to the speaker (physically, in time, or in the conversation).
ese viaje: that trip, a bit more distant, often something both people know about but that is not right here/right now.
aquel viaje: that trip over there / that trip back then, more distant in space or time, or emotionally distant.

In practice, ese viaje is very common for a trip that is being talked about but is not happening right now. Este viaje would be more like a trip that is just about to start or is very present in the speaker’s mind. Aquel viaje often refers to a trip that is far in the past or in a story.

What exactly does tenemos que mean here, and how is this structure formed?

Tenemos que is the first person plural of the construction tener que + infinitive, which expresses obligation or necessity (have to / must).

Formation:

tener (conjugated) + que
- infinitive
tenemos = we have
que = that (here it’s just a linker; it usually isn’t translated directly)
reservar = to book / to reserve

So tenemos que reservar literally is we have to reserve, i.e. we must book.
A common learner mistake is to add de (tenemos que de reservar), which is incorrect. It must be tener que + infinitive, without de.

Why is reservar in the infinitive and not conjugated, like reservamos?

After tener que, the second verb must be in the infinitive:

tenemos que reservar = we have to reserve
Not: tenemos que reservamos

It works similarly to English: you say we have to reserve, not we have to we reserve.

The conjugated verb carrying the tense and person is tenemos. The infinitive reservar just expresses the action that must be done.

Could we say debemos reservar or necesitamos reservar instead of tenemos que reservar? Do they mean the same?

You can, but there are slight differences in nuance:

tenemos que reservar ≈ we have to book; everyday, neutral obligation.
debemos reservar ≈ we must / ought to book; can sound a bit more formal or like a duty or recommendation.
necesitamos reservar ≈ we need to book; focuses more on need than on duty.

All three are correct in this sentence. In casual spoken Spanish, tener que + infinitive is probably the most common way to express this kind of obligation.

Why is it las habitaciones del hotel and not just el hotel?

In Spanish, when you book a hotel, you are usually thought of as booking rooms, not the whole hotel. So:

reservar las habitaciones del hotel = book the hotel rooms
reservar el hotel could be understood as booking the entire hotel, or making an arrangement with that hotel; it’s less precise and sounds unusual for normal travellers.

Using las habitaciones del hotel makes it clear that you are reserving rooms in that hotel, which is what most people actually do.

What does del mean in las habitaciones del hotel?

Del is the contracted form of de + el:

de = of / from
el = the (masculine singular)
de + el → del

So las habitaciones del hotel literally is the rooms of the hotel.

You cannot write de el hotel; in standard Spanish, de el must contract to del whenever el is the masculine singular article (not the pronoun).

Could we say las habitaciones en el hotel instead of las habitaciones del hotel?

You can say las habitaciones en el hotel, but the nuance changes slightly:

las habitaciones del hotel focuses on possession / belonging: the rooms of that hotel (its rooms).
las habitaciones en el hotel focuses on location: rooms in the hotel (physically inside it).

In this sentence, when talking about reservations, las habitaciones del hotel is the most natural choice, because we are booking the hotel’s own rooms, not just any rooms that happen to be located there.

Why is pronto at the end of the sentence? Can it go in other positions?

Putting pronto at the end (…reservar las habitaciones del hotel pronto) is very natural in Spanish, just like …book the hotel rooms soon in English.

You can move it somewhat, for example:

Para ese viaje, pronto tenemos que reservar las habitaciones del hotel. (possible, but less neutral in everyday speech)

However, you normally keep pronto with the verb phrase, and the most common, neutral positions are:

Tenemos que reservar pronto las habitaciones del hotel.
Tenemos que reservar las habitaciones del hotel pronto.

All of these sound natural; the original version is particularly common.

Is there any difference between pronto, temprano, and cuanto antes in this context?

Yes, they are related but not identical:

pronto ≈ soon, fairly soon. General adverb of time.
- …tenemos que reservar… pronto = we have to book soon.
temprano ≈ early (in the day or earlier than usual).
- More about time of day or being early, not just soon.
- Reservamos temprano mañana = we book early tomorrow.
cuanto antes ≈ as soon as possible / the sooner the better.
- Stronger sense of urgency: …tenemos que reservar… cuanto antes.

In your sentence, pronto is the natural, neutral choice if you just mean soon without adding extra urgency.