Quiero bajar del tren en la siguiente parada.

Because Spanish often drops subject pronouns when the verb already makes the subject clear.

• Quiero already means I want
• So (Yo) quiero bajar del tren... and Quiero bajar del tren... are both correct

Including yo can add emphasis, contrast, or clarity, but it is not necessary in a normal sentence.

Quiero is the first-person singular present indicative form of querer.

So it means:

• I want
• I would like in some contexts, though querer is often more direct than English would like

Other forms of querer include:

• quieres = you want
• quiere = he/she/it wants, you want (formal)
• queremos = we want

After querer, Spanish normally uses another verb in the infinitive.

Pattern:

• querer + infinitive

So:

• Quiero bajar
• Quiero comer
• Quiero salir

This is very similar to English I want to + verb, except Spanish does not need a separate word for to here.

Because de + el contracts to del in Spanish.

So:

• de el tren → del tren

This contraction is mandatory in normal Spanish.

A similar common contraction is:

• a + el → al

For example:

• Voy al tren
• Bajo del tren

Yes, all of these can appear, but they are not exactly identical in feel.

• bajar del tren = to get off the train
• bajarse del tren = to get off the train, often very natural in everyday speech
• salir del tren = to leave/exit the train

For transport, bajar (del tren, del autobús, del metro) is very common.

In everyday Spanish, many speakers would also say:

• Quiero bajarme del tren en la siguiente parada

That sounds very natural too. The version without me is still correct.

In bajarse, the reflexive pronoun often makes the action sound more like getting oneself off the train. In practice, with transport, bajar and bajarse are often both used.

So:

• Quiero bajar del tren
• Quiero bajarme del tren

Both can be natural. The reflexive version is especially common in speech.

Because en is used here to mean at the next stop, meaning the action happens there.

• bajar en una parada = get off at a stop

Using a would suggest movement toward a destination, which is not the idea here.

Compare:

• Bajo en la siguiente parada = I get off at the next stop
• Voy a la siguiente parada = I go to the next stop

Yes, in this context they are very close in meaning.

• la siguiente parada = the following stop / the next stop
• la próxima parada = the next stop

In everyday use, both are natural. Many learners hear próxima parada often in announcements, but siguiente parada is also completely normal.

Because many adjectives in Spanish can go after or before the noun, but some combinations are more natural in one position.

• la siguiente parada is the standard, very common order
• la parada siguiente is possible, but less usual here

For a learner, la siguiente parada is the safest and most natural choice.

Yes, but the original order is the most neutral.

Neutral:

• Quiero bajar del tren en la siguiente parada.

You could also say:

• En la siguiente parada quiero bajar del tren.

That version puts more focus on en la siguiente parada.

Spanish word order is flexible, but not completely free. The original sentence is the most straightforward everyday version.

Yes, if the context is already clear.

If everyone knows you are on a train, bus, or metro, then:

• Quiero bajar en la siguiente parada

can sound perfectly natural.

But if you want to be explicit, especially for a learner, del tren makes the meaning clearer.

It is natural and correct in Spain.

That said, in everyday conversation, people might also say:

• Quiero bajarme en la siguiente parada.
• Me quiero bajar en la siguiente parada.
• Me bajo en la siguiente parada.
  if they are stating a decision rather than saying I want to

So your sentence is good Spanish, but real speech may use slightly different versions depending on style and context.

A few useful points:

• quiero: roughly KYEH-ro
  • quie- sounds like kye
• bajar: roughly ba-HAR in Spain
  • the j is a strong throaty sound, not an English h exactly
• tren: one syllable, roughly tren
• siguiente: roughly see-GYEN-te
  • the gui here sounds like gye
  • the u is silent in gui unless it has a dieresis, as in güi

The stress falls on:

• QUIE-ro
• ba-JAR
• TREN
• si-GUIEN-te
• pa-RA-da

No, not in this sentence.

• parada is a noun: stop
• parar is a verb: to stop

So:

• en la siguiente parada = at the next stop

If you used parar, the grammar would no longer work in the same way.