После дождя муравьи быстро вернулись в муравейник, а жук остался на камне.

Because после requires the genitive case.

• дождь = rain (dictionary form, nominative)
• дождя = genitive singular

So:

• после дождя = after the rain

This is a very common pattern in Russian:

• после урока = after the lesson
• после работы = after work
• после обеда = after lunch

So the learner should remember: после + genitive.

Муравьи means ants, so it is plural.

Because the subject is plural, the past-tense verb is also plural:

• вернулся = he returned
• вернулась = she returned
• вернулось = it returned
• вернулись = they returned

So:

• муравьи вернулись = the ants returned

In the Russian past tense, verbs agree with the subject in number, and in the singular they also agree in gender.

Вернулись is the perfective past form of вернуться, meaning the action is viewed as completed: they returned and got back.

In this sentence, that makes sense because the ants finished returning to the anthill.

Compare:

• вернулись = returned, got back
• возвращались = were returning / used to return

So вернулись presents the return as a completed event after the rain.

Also, вернуться is reflexive because returning is expressed in Russian with the -ся / -сь form.

This is about both preposition choice and case.

1. в муравейник

Here the meaning is motion into somewhere, so Russian uses:

• в + accusative

So:

• муравейник is the accusative form here
• в муравейник = into the anthill

2. на камне

Here there is location, not motion. The beetle remained on the stone. So Russian uses:

• на + prepositional for location

So:

• камне is the prepositional form of камень
• на камне = on the stone

A useful contrast:

• на камень = onto the stone, motion
• на камне = on the stone, location

Because жук is:

• singular
• masculine

So the past tense of остаться must be masculine singular:

• остался = he/it remained

Compare:

• жук остался = the beetle remained
• муха осталась = the fly remained
• насекомое осталось = the insect remained
• жуки остались = the beetles remained

So the ending -ся is part of the verb, and -л + masculine form gives остался.

А often connects two clauses by showing a contrast or a change of focus.

Here:

• муравьи быстро вернулись в муравейник
• а жук остался на камне

This means something like:

• the ants quickly returned to the anthill, whereas the beetle stayed on the stone

Why not и?

• И just means and, with no real contrast.

Why not но?

• Но means but and often sounds like a stronger contradiction.

Here а is very natural because the sentence contrasts what the ants did with what the beetle did.

Быстро is an adverb meaning quickly.

Russian word order is more flexible than English, so быстро can move around depending on emphasis. In this sentence:

• муравьи быстро вернулись в муравейник

is the most neutral and natural order.

Other orders are possible, for example:

• муравьи вернулись быстро
• быстро муравьи вернулись в муравейник

But they may sound more marked or emphasize a different part of the sentence.

So the main point is:

• быстро modifies the verb вернулись
• its position here is normal and natural

The dictionary form is камень = stone.

After на when it means on in a location sense, Russian usually uses the prepositional case.

So:

• камень → на камне

This change is irregular enough that it is worth memorizing:

• о камне = about the stone
• на камне = on the stone

Many masculine nouns ending in -ь change form in this way in the prepositional.

Yes. Муравейник means anthill.

It is built from муравей meaning ant, plus the suffix -ник, which often forms nouns for places, containers, or things associated with something.

So for a learner, it can be helpful to see the connection:

• муравей = ant
• муравейник = anthill

In the sentence, в муравейник means into the anthill, with the accusative after в because it shows direction.

Because the sentence describes what happened after the rain.

The two actions are presented as completed past events:

• муравьи быстро вернулись = the ants returned
• жук остался = the beetle remained

Russian past tense is formed differently from English. It does not use a separate word like did. Instead, the verb itself changes form:

• вернуться → вернулись
• остаться → остался

So once you identify the subject and the verb ending, you can see who did the action and whether it is singular or plural.

Yes, it could, but the meaning would be less specific.

For example:

• После дождя муравьи быстро вернулись, а жук остался.

This is grammatical, but it no longer says where the ants returned to or where the beetle stayed.

The original sentence includes those phrases to make the scene clear:

• в муравейник = destination
• на камне = location

So they are not required for grammar, but they are important for the full meaning of the sentence.