Learn Hardcore Spanish (Spain): Caminamos despacio por el callejón resbaladizo para no caernos. - We walk slowly through the slippery alley so we don’t fall.

Por here means “through/along,” i.e., movement within a place: We walked along/through the alley.
En marks location, not path: Estamos en el callejón = We are in the alley.
A/al marks destination toward a place: Vamos al callejón = We’re going to the alley. So with caminar to express path, Spanish prefers por.

Is caminamos present (“we walk”) or past (“we walked”)?

It can be either. 1st‑person plural present and preterite of caminar are identical (caminamos). Context or time markers show which is meant:

Present: Siempre caminamos despacio...
Preterite: Ayer caminamos despacio... If you want “ongoing past,” use the imperfect: Caminábamos despacio...

Why despacio and not lentamente or despacito?

Despacio = “slowly,” very common and neutral.
Lentamente = “slowly,” a bit more formal/technical but fine.
Despacito = diminutive, often “very slowly/gently” or adds a softer tone; informal. All three can work; despacio is the most everyday choice.

What exactly is a callejón? How is it different from calle, calleja, or pasillo?

Callejón: a narrow alley. Not necessarily a dead end unless you say callejón sin salida.
Calle: a street.
Calleja: a very narrow street/lane (common in parts of Spain).
Pasillo: a corridor/hallway inside a building.

Why does resbaladizo come after the noun? How does it agree?

Most descriptive adjectives follow the noun: el callejón resbaladizo. It agrees in gender/number:

el callejón resbaladizo
la acera resbaladiza
los callejones resbaladizos
las aceras resbaladizas

Are there regional alternatives to resbaladizo?

Yes. In much of Latin America you’ll also hear resbaloso/resbaladoso. In Spain, resbaladizo is standard. Deslizante exists but is more technical (e.g., “non-slip surfaces”).

What does para no do here? Could I use para que no instead?

Para + infinitive expresses purpose when the subject is the same: Caminamos... para no caernos.
Para que + subjunctive is used when the subject changes: Caminamos... para que los niños no se caigan. With the same subject, both are possible, but para + infinitive is simpler: Caminamos... para no caernos / para que no nos caigamos.

Why is the pronoun nos attached to caer (caernos)? Can it go elsewhere?

With an infinitive, object/reflexive pronouns attach to the end: caernos. The negative no goes before the verb phrase: para no caernos. You cannot say para no nos caer. If you restructure with a finite verb, the pronoun goes before it: para que no nos caigamos.

What’s the difference between caer and caerse?

Caerse (pronominal) is very common for unintentional/accidental falling of people/animals: Me caí = I fell (down).
Caer without se can be intransitive (Las hojas caen = The leaves fall) or transitive (“to drop” something: Caí el vaso is rare; more often se me cayó el vaso). In your sentence, para no caer and para no caernos are both acceptable; caerse sounds more colloquial/personal.

Can I leave out nos and just say para no caer?

Yes. Para no caer is grammatical because the subject (“we”) is understood from the main clause. Para no caernos makes it explicitly about us and is very idiomatic.

Could I use evitar instead: para evitar caernos?

Yes: Caminamos despacio... para evitar caernos. Slightly more formal/explicit. With a clause: para evitar que nos caigamos.

Pronunciation tips (Spain)

C before e/i and z = “th” sound: de-spa-thyo (despacio), res-bala-dhee-tho (resbaladizo).
J = harsh h: ca-ye-HON (callejón).
LL usually sounds like English y: ca-ye- (calle-). Some speakers pronounce it differently.
Stress: ca-mi-NÁ-mos; des-PA-cio; ca-lle-JÓN; res-ba-la-DI-zo; ca-ÉR-nos (two syllables: ca-ER).
Link por el smoothly: po-rel.

Could I say a través de instead of por?

Generally no for walking along an alley. A través de means “through” in the sense of passing across/through something (a barrier, medium, or expanse): a través del bosque/la ventana. For routes/streets, por is idiomatic.

How would the pronoun change with different subjects?

Match the reflexive to the subject:

Yo: para no caerme
Tú: para no caerte
Él/Ella/Usted: para no caerse
Nosotros/as: para no caernos
Vosotros/as (Spain): para no caeros
Ellos/Ellas/Ustedes: para no caerse

Could I use andar instead of caminar?

Yes: Andamos despacio... is natural in Spain. Andar can also mean “to function/to be around,” but for “to walk,” andar and caminar are often interchangeable.