Дождь стих, и мы пошли в парк.

Стих is the past tense of стихнуть, a verb meaning to die down, to subside, or to let up.

So Дождь стих means that the rain became weaker and stopped enough for the situation to change. It often sounds a bit more natural for weather, noise, wind, pain, etc. than a very literal stopped.

Related examples:

• Ветер стих — the wind died down
• Шум стих — the noise died down

Because the subject is дождь, which is a masculine singular noun.

In the past tense, Russian verbs agree with the subject in gender and number:

• masculine: стих
• feminine: стихла
• neuter: стихло
• plural: стихли

Since дождь is masculine, the correct form is стих.

Дождь is in the nominative case because it is the subject of the sentence — the thing performing the action of стих.

In Дождь стих, the structure is very straightforward:

• дождь = subject
• стих = verb

So this is basically The rain subsided.

Because this sentence joins two independent clauses:

• Дождь стих
• мы пошли в парк

Each part could stand on its own as a complete sentence, so Russian normally uses a comma before и in this situation.

This is similar to English:

• The rain let up, and we went to the park.

Пошли is usually used here because it is perfective and often means set off / started going / went as a complete action.

Compare:

• мы пошли в парк — we went to the park / we set off for the park
• мы шли в парк — we were walking to the park / we went on foot to the park, with emphasis on the process

In this sentence, the speaker is telling a sequence of completed events:

1. the rain stopped
2. then we went to the park

That makes пошли the natural choice.

Not always in a strict physical sense.

Historically and grammatically, пойти / идти are verbs of going associated with going on foot, and that basic idea is still important. But in everyday Russian, пошли is also often used more broadly to mean let’s go, we went, or we headed off, especially when the exact mode of transport is not the main point.

Still, if you specifically want to say we went by vehicle, Russian often uses another verb, such as:

• поехали — went by transport / drove / rode

So in мы пошли в парк, the default feeling is that they went there themselves, very likely on foot.

Because в парк shows motion to a place, so парк is in the accusative case.

Russian uses:

• в + accusative for motion into / to
• в + prepositional for location in / inside

Compare:

• Мы пошли в парк — we went to the park
• Мы были в парке — we were in the park

This is a very important pattern in Russian.

Because парк is an inanimate masculine noun, and for inanimate masculine nouns the accusative singular usually looks the same as the nominative singular.

So:

• nominative: парк
• accusative: парк

If it were an animate masculine noun, the accusative would usually match the genitive instead.

Yes, мы could be omitted in many contexts.

Russian often drops subject pronouns when the verb ending already makes the subject clear:

• Дождь стих, и пошли в парк.

Since пошли clearly shows we from context, this can work.

However, мы is often kept:

• for clarity
• for emphasis
• because it sounds natural in normal speech

So both are possible, but мы пошли в парк is completely normal.

Yes.

• стих comes from стихнуть — perfective
• пошли comes from пойти — perfective

That matters because the sentence describes completed events in sequence:

1. the rain subsided
2. we went to the park

Perfective verbs are very common in this kind of narrative chain.

Not by itself, usually no.

Перестать normally needs an infinitive:

• Дождь перестал идти — the rain stopped falling
• Дождь перестал by itself sounds incomplete to many speakers

By contrast, Дождь стих is complete and natural on its own.

There is also a nuance:

• перестал идти = stopped falling
• стих = died down / subsided / let up

So стих is especially idiomatic here.

No, Russian word order is fairly flexible, though the original sentence is the most neutral.

Дождь стих, и мы пошли в парк sounds like a normal, straightforward narrative.

Other orders are possible for emphasis, for example:

• Мы пошли в парк, когда дождь стих — more explicitly We went to the park when the rain let up
• В парк мы пошли, когда дождь стих — emphasis on to the park

But the original version is probably the best default phrasing for a learner to remember.