Ese coche salpica agua cuando pasa por la calle mojada.

Ese means that, while este means this.

So:

• este coche = this car (near the speaker)
• ese coche = that car (a bit farther away, or not right by the speaker)

In modern Spanish, ese is very common for that. A learner may also see aquel coche, which usually refers to something even farther away or more distant in context.

In Spain, coche is the normal everyday word for car.

• coche = standard in Spain
• carro = more common in many Latin American varieties, but in Spain it usually does not mean a normal car in everyday speech

So if you are learning Spanish from Spain, coche is the best choice here.

Salpicar means to splash or to splatter.

In this sentence, Ese coche salpica agua means the car throws water outward as it moves, for example from puddles on a wet street.

Other examples:

• El niño salpica agua en la piscina. = The child splashes water in the pool.
• La pintura salpicó la pared. = The paint splattered the wall.

Here, agua is being used in a general, non-specific way, so Spanish often leaves out the article.

• salpica agua = splashes water
• salpica el agua would sound more like it splashes the water, referring to some specific water already identified in context

In English we also often say splashes water, not necessarily splashes the water. So the Spanish choice is very natural.

Spanish often leaves out subject pronouns because the verb ending already shows who is doing the action.

• pasa can mean he/she/it passes
• here, the subject is already clear: ese coche

So:

• Ese coche salpica agua cuando pasa... = natural
• Ese coche salpica agua cuando él pasa... = unnecessary here, and a bit unnatural unless you want special emphasis

Yes. The subject of pasa is still ese coche.

So the structure is:

• Ese coche = subject
• salpica agua = main action
• cuando pasa por la calle mojada = when it goes/passes along the wet street

Even though the subject is not repeated, Spanish understands it from the context.

The present tense here expresses a general or repeated action.

It suggests something like:

• That car splashes water when it goes down the wet street
• Whenever that car passes along the wet street, it splashes water

Spanish uses the present tense a lot for habitual actions and general truths, just like English does.

Por often means through, along, or down when talking about movement.

So:

• pasa por la calle = it goes/passes along the street
• está en la calle = it is in/on the street

Here the car is moving along the street, so por is the natural preposition.

Because mojada describes calle, and calle is feminine singular.

Agreement in Spanish:

• calle = feminine singular
• adjective must match it
• so: calle mojada

Compare:

• el coche mojado = the wet car
• la calle mojada = the wet street

Yes, mojada means wet.

It comes from the verb mojar = to wet / to make wet.
The adjective form changes for gender and number:

• mojado = wet (masculine singular)
• mojada = wet (feminine singular)
• mojados / mojadas = wet (plural)

In this sentence, it describes the street as wet, probably from rain or puddles.

Yes. In context, pasa por la calle can be translated in several natural ways:

• passes along the street
• goes down the street
• drives through the street
• passes through the wet street (depending on context)

Spanish pasar por is flexible. The exact English translation depends on what sounds most natural in the situation.

This is a very normal Spanish sentence pattern:

• Ese coche = subject
• salpica = verb
• agua = direct object
• cuando pasa por la calle mojada = time clause

So the structure is basically:

Subject + verb + object + subordinate clause

Spanish word order can be flexible, but this version is straightforward and neutral.

Sometimes, yes, but street is usually the most direct translation of calle.

• calle = street
• carretera = road / highway

If you say por la calle mojada, the image is usually of a street in a town or city, not a highway or country road. So street fits best here.

A few possible variations are:

• Ese coche salpica agua al pasar por la calle mojada.
  = That car splashes water when passing along the wet street.

• Ese coche salpica a la gente cuando pasa por la calle mojada.
  = That car splashes people when it goes down the wet street.

• Ese coche salpica mucha agua cuando pasa por la calle mojada.
  = That car splashes a lot of water when it goes down the wet street.

Your original sentence is already completely natural. These are just useful variations.