Learn Hardcore Spanish (Latin America): A pesar de la lluvia camino por la calle cada día. - Despite the rain, I walk on the street every day.

A pesar de literally means “in spite of” or “despite.” It’s a prepositional phrase that must be followed by a noun or noun phrase. In this case, la lluvia (the rain) is that noun.
Example:

A pesar de la lluvia, salimos a jugar. = In spite of the rain, we went out to play.

Why isn’t there a que after a pesar de in this sentence?

When you follow a pesar de with a noun (la lluvia), you don’t use que. If you want to introduce a full clause, you add que and a conjugated verb:

A pesar de que llovía, caminé igual. = Despite the fact that it was raining, I walked anyway.

Why is the subject yo omitted before camino?

Spanish often drops (omits) subject pronouns because the verb ending already tells you who’s doing the action. Camino ends in -o, which uniquely marks the first person singular present. Adding yo is not wrong, but it’s redundant:

(Yo) camino por la calle cada día.

Why is it camino por la calle and not camino en la calle?

Por expresses movement through, along, or by a place.
En indicates location or position (static).
So caminar por la calle means you’re walking along/through the street, whereas caminar en la calle would simply mean you’re walking somewhere within the street, focusing on the location rather than the path.

What’s the difference between cada día and todos los días?

Both mean “every day,” but there’s a slight nuance:

Cada día emphasizes the idea of each individual day.
Todos los días stresses the habitual frequency (all the days together).
In practice, they’re interchangeable:
Camino cada día.
Camino todos los días.

Why do we use la before lluvia and calle?

Spanish uses definite articles before general or abstract nouns where English often omits them. Here, you’re talking about the rain in general and the street as a known route:

la lluvia = “the rain” (in general)
la calle = “the street” (a specific, understood street)

Can I reorder the sentence and say Camino por la calle cada día a pesar de la lluvia?

Yes. Spanish word order is flexible. Moving a pesar de la lluvia to the end still makes sense. However, placing it at the beginning (as in the original) gives more emphasis to the contrast (“In spite of the rain…”).

Why does día have an accent on the í?

Día is a two-syllable word (di-a) with stress on the first syllable, breaking what would otherwise be a diphthong. According to Spanish spelling rules, you need the written accent to:

Mark the stress on the penultimate syllable when it doesn’t follow the default pattern.
Indicate that i and a form two separate sounds (a hiatus), not a single diphthong.