Quiero acampar en la montaña con mi hermana este fin de semana.

In Spanish, subject pronouns are often omitted because the verb ending already shows who is doing the action.

• quiero = I want
• The -o ending tells you it is yo

So Quiero acampar... is completely natural.
You could say Yo quiero acampar... if you want extra emphasis, for example to contrast with someone else:

• Yo quiero acampar, pero mi hermana no. = I want to camp, but my sister doesn’t.

This is a very common Spanish structure:

• querer + infinitive = to want to do something

So:

• quiero = I want
• acampar = to camp

Together, quiero acampar means I want to camp.

This works with many other verbs too:

• Quiero comer = I want to eat
• Quiero viajar = I want to travel
• Quiero dormir = I want to sleep

Yes. Acampar is a regular -ar verb.

Its infinitive is acampar = to camp.

Some present tense forms are:

• yo acampo = I camp
• tú acampas = you camp
• él/ella acampa = he/she camps
• nosotros acampamos = we camp
• vosotros acampáis = you all camp (Spain)
• ellos acampan = they camp

In your sentence, it stays in the infinitive because it follows quiero.

Because en usually expresses location, while a often expresses movement toward a destination.

• acampar en la montaña = to camp in the mountains / in the mountain area
• ir a la montaña = to go to the mountains

So in your sentence, the important idea is the place where the camping happens, not just movement toward it.

A useful comparison:

• Voy a la montaña. = I’m going to the mountains.
• Acampo en la montaña. = I camp in the mountains.

Yes, las montañas could also work, but the meaning shifts slightly.

• en la montaña often means in the mountains / in the mountain area in a general sense
• en las montañas sounds more literally like in the mountains

Both are possible depending on context.
In everyday Spanish, la montaña is often used in a broad, natural way to refer to a mountainous area or the countryside.

So acampar en la montaña sounds very normal.

Because mi without an accent is the possessive adjective meaning my.

• mi hermana = my sister

mí with an accent is a pronoun meaning me, usually used after prepositions:

• para mí = for me
• sin mí = without me

So:

• mi hermana = correct
• mí hermana = incorrect

Yes. Spanish word order is flexible, although some orders sound more natural than others.

Your sentence:

• Quiero acampar en la montaña con mi hermana este fin de semana.

You could also say:

• Quiero acampar con mi hermana en la montaña este fin de semana.

Both are correct. The difference is mostly about emphasis and rhythm.
Spanish often moves phrases around more freely than English, as long as the meaning stays clear.

In Spanish, time expressions often do not need a preposition where English might use one.

So:

• este fin de semana = this weekend
• esta semana = this week
• este año = this year

Using en here would usually sound unnatural for this meaning.

So the sentence correctly says:

• ...este fin de semana = ...this weekend

Literally, fin de semana means end of week, but it is the normal Spanish expression for weekend.

• el fin de semana = the weekend
• este fin de semana = this weekend
• los fines de semana = weekends

In Spain, this is the standard everyday expression.

Primarily, quiero expresses a desire or intention:

• Quiero acampar = I want to camp

Depending on context, it can also imply a possible plan, but it is not as definite as saying:

• Voy a acampar = I’m going to camp
• Acamparé = I will camp

So quiero acampar sounds like a wish, intention, or idea, rather than a fully fixed plan.

In standard Spanish from Spain, quiero is pronounced approximately like KYEH-ro.

A few points:

• qu before i gives a hard k sound
• ie forms a diphthong, so it glides together
• the r in quiero is a light tapped r, not the strong rolled rr

So it is not pronounced like English queer-oh, but more like KYEH-ro.

The ñ is a separate Spanish letter and sound. It is similar to the ny sound in canyon.

So montaña is pronounced approximately:

• mon-TA-nya

The stress is on the second syllable:

• mon-TA-ña

This sound is important because n and ñ are different in Spanish.

Yes. Quisiera acampar... is possible, but it sounds more polite, softer, or more tentative.

Compare:

• Quiero acampar... = I want to camp...
• Quisiera acampar... = I’d like to camp...

So if you are simply stating what you want, quiero is the most direct and natural choice.
If you want to sound more polite or less direct, quisiera can work well.