A pesar de que el camino hasta la cima es largo, mi prima quiere subir sin quejarse.

A pesar de que means in spite of the fact that, even though, or although.

In this sentence, it introduces a contrast:

• A pesar de que el camino hasta la cima es largo = Even though the path to the summit is long
• mi prima quiere subir sin quejarse = my cousin wants to go up / climb without complaining

So the idea is: the climb is long, but that does not stop her.

After a pesar de que, Spanish can use either the indicative or the subjunctive, depending on how real or certain the information is.

Here, es largo uses the indicative because the speaker presents the path being long as a real, known fact.

• A pesar de que... es largo = the speaker treats it as true and definite

If you used the subjunctive, such as sea largo, it would sound more hypothetical, uncertain, or less firmly stated.

They are often very similar, and in many cases both can mean although / even though.

So this sentence could also be:

• Aunque el camino hasta la cima es largo, mi prima quiere subir sin quejarse.

However, a pesar de que can feel a little more explicit, like despite the fact that.
Aunque is often more common and slightly more flexible in everyday speech.

Spanish usually uses definite articles more often than English.

• el camino = the path
• la cima = the summit / the top

Even where English might sometimes say path or summit more generally, Spanish often prefers the article when referring to a specific thing understood from the context.

Hasta means up to, as far as, or until, depending on context.

Here:

• hasta la cima = to the summit / all the way to the top

So el camino hasta la cima means the path up to the summit or the route to the top.

Because largo means long, and it describes the length of the path.

• un camino largo = a long path
• una película larga = a long film
• una conversación larga = a long conversation

It agrees with camino, which is masculine singular, so it becomes largo.

Yes. Prima is a female cousin.

• mi prima = my female cousin
• mi primo = my male cousin

English uses cousin for both, but Spanish distinguishes the gender.

Because querer is followed directly by an infinitive.

• quiere subir = wants to climb / wants to go up
• quiero comer = I want to eat
• queremos salir = we want to leave

No extra preposition is needed after querer when another verb follows.

Subir literally means to go up, to climb, or to ascend.

In this sentence, because we are talking about the path to the summit, subir means something like:

• to climb up
• to go up
• to make the ascent

The most natural English translation depends on context.

After sin, Spanish often uses the infinitive when the subject is the same as in the main clause.

Here, the person who wants to climb and the person who doesn’t complain is the same person: mi prima.

So:

• mi prima quiere subir sin quejarse = my cousin wants to climb without complaining

Using sin que + subjunctive is more common when the subject changes:

• Sube sin que nadie se queje = She climbs without anyone complaining

So in your sentence, sin quejarse is the natural structure.

Because quejarse is a pronominal verb. The full verb is quejarse, not just quejar.

It means to complain.

When a pronominal verb is in the infinitive, the pronoun stays attached to the end:

• quejarse
• levantarse
• irse
• dormirse

So sin quejarse is literally without complaining oneself, though in natural English we just say without complaining.

In normal modern usage, yes: the common verb is quejarse.

Examples:

• Se queja mucho = He/She complains a lot
• No quiero quejarme = I don’t want to complain
• Se quejaron del frío = They complained about the cold

So learners should treat quejarse as the standard dictionary form.

Because the sentence begins with a subordinate clause:

• A pesar de que el camino hasta la cima es largo, ...

In Spanish, when this kind of introductory clause comes first, it is normal to separate it from the main clause with a comma.

So the comma marks the break between:

1. the contrast clause
2. the main statement

Yes. You can also say:

• Mi prima quiere subir sin quejarse, a pesar de que el camino hasta la cima es largo.

This means the same thing.

The version with A pesar de que... at the beginning puts more emphasis on the contrast from the start. The version with the main clause first sounds a bit more straightforward.

Yes, depending on the exact situation.

For example:

• sendero = trail, footpath
• ruta = route
• subida = ascent, uphill stretch

But camino is a very common and general word for path, road, or way, so it works well here.