Después del trueno, vimos un relámpago muy cerca del valle y entramos en casa enseguida.

Because de + el contracts to del in Spanish.

So:

• de el trueno → del trueno

This contraction is mandatory whenever de is followed by the masculine singular article el, unless El is part of a proper name, such as de El Escorial.

They refer to two different parts of a storm:

• trueno = thunder (the sound)
• relámpago = lightning or flash of lightning (what you see)

So the sentence is talking about hearing/being after the thunder, then seeing lightning.

They are in the preterite because the sentence describes completed events in a sequence:

1. after the thunder,
2. we saw lightning,
3. we went inside.

The preterite is the normal tense for actions that happened as finished events in the past.

• vimos = we saw
• entramos = we went in / entered

If the sentence were describing background or ongoing actions, Spanish would be more likely to use the imperfect.

Yes. Vimos is the 1st person plural preterite of ver.

The preterite of ver is:

• vi = I saw
• viste = you saw
• vio = he/she/it saw
• vimos = we saw
• visteis = you all saw
• vieron = they saw

For a learner, vimos can look a bit unusual because ver is short, but this is the standard form.

Spanish usually leaves out subject pronouns when the verb already makes the subject clear.

• vimos already tells you it means we saw
• entramos already tells you it means we entered

So nosotros is unnecessary unless you want emphasis or contrast.

For example:

• Nosotros vimos un relámpago, no ellos.
  = We saw lightning, not them.

But in a normal sentence, omitting the pronoun is more natural.

Because un introduces something not previously identified: a lightning flash / a bolt of lightning.

Using el relámpago would suggest a specific, already known lightning flash, which usually would not fit as naturally here.

So:

• vimos un relámpago = we saw a flash of lightning
• vimos el relámpago = we saw the flash of lightning

In this context, the indefinite article is the normal choice.

Because cerca normally goes with de in Spanish:

• cerca de = near / close to

So:

• cerca del valle = near the valley

And del is again just de + el.

Also, muy intensifies cerca:

• cerca del valle = near the valley
• muy cerca del valle = very near the valley

Because after cerca, Spanish normally uses de, not a.

Correct:

• cerca del valle
• cerca de la casa
• cerca de nosotros

Not standard here:

• cerca al valle

For English speakers, this is worth remembering because English says close to, but Spanish says cerca de.

In the sentence, muy cerca del valle most naturally describes where the relámpago was seen: the lightning was very near the valley.

So the structure is understood as:

• vimos [un relámpago muy cerca del valle]

That said, context always matters. In real life, a listener may also understand it more generally as part of the scene. But grammatically, it most naturally goes with relámpago.

Because en casa is a very common Spanish expression meaning at home / home / into the house depending on context.

Here, entramos en casa means something like we went inside the house / we went home inside.

Using en la casa is possible in some situations, but it sounds more specific and literal, as if you are emphasizing the physical building. En casa is the more natural everyday expression when talking about home.

Yes, in some varieties of Spanish you may hear entrar a with places, but in Spain entrar en is especially common and standard.

So for Spanish from Spain, entramos en casa is a very natural choice.

A useful rule for learners is:

• entrar en
  • place

Examples:

• entrar en casa
• entrar en el coche
• entrar en la habitación

Enseguida means immediately, right away, or straight away.

Here it shows that they went inside very quickly after seeing the lightning.

In Spain, enseguida is very common in everyday speech. It can sometimes mean very soon depending on context, but in this sentence it clearly means without delay.

Spanish adverbs like enseguida are quite flexible in position. Putting it at the end is very natural and emphasizes the quick reaction.

These are all possible:

• entramos en casa enseguida
• enseguida entramos en casa
• entramos enseguida en casa

The version in your sentence sounds smooth and idiomatic.

Because Después del trueno is an introductory time phrase placed before the main clause.

The comma helps separate that opening element from the main action:

• Después del trueno, vimos...

In short sentences, Spanish punctuation can sometimes be flexible, but the comma here is very normal and helps readability.

Because it refers to one specific clap or rumble of thunder.

Spanish often uses the singular when talking about one event:

• Después del trueno = after the thunderclap / after the thunder

If there had been several separate thunderclaps being emphasized, you might see a plural expression, but the singular is perfectly natural here.