No sé si mi hermana ya ha reservado el hotel.

Here si means if / whether in an indirect question: I don’t know if / whether...

So No sé si mi hermana... means I don’t know whether my sister...

Spanish uses si both for:

• whether / if in indirect questions: No sé si viene
• if in conditions: Si llueve, nos quedamos en casa

The meaning comes from the context.

Because they are different words:

• si = if / whether
• sí = yes
• sé = I know
• se = a pronoun, as in se llama

So in your sentence:

• No sé = I don’t know
• si = if / whether

The accent on sé helps distinguish it from se.

Because Spanish usually uses saber for knowing a fact, a piece of information, or the answer to something.

• saber = to know information
• conocer = to know a person, place, or be familiar with something

Here the speaker does not know whether the booking has happened, so saber is the correct verb:

• No sé si... = I don’t know if...

You would use conocer in sentences like:

• Conozco a tu hermana
• Conozco ese hotel

Because Spanish often leaves out subject pronouns when the subject is already clear.

In this sentence, mi hermana already tells you who the subject is, so ella is unnecessary:

• No sé si mi hermana ya ha reservado el hotel

Adding ella would usually sound redundant unless you want special emphasis:

• No sé si ella ya ha reservado el hotel
  This could imply contrast, like I don’t know if she has booked it, but someone else may have.

Ha reservado is the present perfect:

• ha = has
• reservado = booked / reserved

In Spain, this tense is very common for past actions that are:

• connected to the present
• recent
• relevant now

So ya ha reservado el hotel suggests something like has she booked it yet / by now?

By contrast, reservó is the preterite and presents the action more as a finished past event.

In many parts of Latin America, people often use reservó in places where Spain would naturally prefer ha reservado.

Yes, very often.

In Spain, speakers commonly use the present perfect for recent or present-relevant past actions:

• Ya ha reservado el hotel
• Esta mañana he hablado con Ana

In much of Latin America, the preterite is often more common in everyday speech in these same situations:

• Ya reservó el hotel
• Esta mañana hablé con Ana

So your sentence sounds very natural for Spanish from Spain.

Ya means already.

It shows that the speaker is thinking about whether the action has happened by now. It often carries the idea that the action was expected or is relevant at this point.

So:

• ha reservado el hotel = has booked the hotel
• ya ha reservado el hotel = has already booked the hotel

Without ya, the sentence is still correct, but it loses that already / by now nuance.

That is a very natural position in Spanish.

In mi hermana ya ha reservado el hotel, ya comes before the verbal group and modifies the whole action.

Other placements are also possible, for example:

• Mi hermana ha reservado ya el hotel

This is also correct, but the rhythm and emphasis are slightly different. For most learners, ya ha reservado is a very useful default pattern.

Because no sé si introduces an indirect yes/no question, and Spanish normally uses the indicative after it.

So:

• No sé si mi hermana ya ha reservado el hotel

This does express uncertainty, but it is not the kind of uncertainty that automatically triggers the subjunctive. Spanish treats it as I don’t know whether this fact is true.

Compare:

• No sé si viene = I don’t know if he is coming
• No sé si ha reservado = I don’t know if she has booked

So although the speaker is unsure, the clause after si is normally in the indicative.

Because el hotel refers to a specific hotel that the speaker has in mind.

It suggests something like:

• the hotel for the trip
• the hotel already discussed
• the hotel they were supposed to book

If the speaker meant some hotel or other, without specifying which one, then un hotel would be possible:

• No sé si mi hermana ya ha reservado un hotel

That means she may have booked a hotel, but not necessarily a particular one already identified in the conversation.

No. In ha reservado, reservado is a past participle used with haber to form the present perfect, and with haber the participle does not agree in gender or number.

So you say:

• ha reservado el hotel
• ha reservado la habitación
• ha reservado las habitaciones

Not:

• ha reservada
• ha reservadas

Agreement happens when a participle is used more like an adjective, but not in the normal perfect tenses with haber.