Когда карусель остановилась, дети ещё долго смеялись и махали маме.

Because the sentence begins with a subordinate clause introduced by когда (when):

Когда карусель остановилась,
дети ещё долго смеялись и махали маме.

In Russian, a subordinate clause is normally separated from the main clause by a comma, just like in English: When the carousel stopped, the children...

The verb is agreeing with карусель, which is a feminine singular noun.

• карусель = feminine, singular
• past tense verbs in Russian agree in gender and number

So:

• остановился = masculine singular
• остановилась = feminine singular
• остановились = plural

Since карусель is feminine singular, остановилась is the correct form.

Because the verb is остановиться, a reflexive verb. In this sentence it means to stop.

Russian often uses a reflexive form where English does not. Compare:

• остановить = to stop something
• остановиться = to stop, come to a stop

So:

• Карусель остановилась = The carousel stopped
• Кто-то остановил карусель = Someone stopped the carousel

Here the carousel itself came to a stop, so the reflexive verb is used.

Because the sentence refers to a completed event: the carousel reached the point of stopping.

• останавливаться / останавливаться (imperfective) would focus on the process or repeated stopping
• остановиться (perfective) focuses on the completed result

In this sentence, the stopping happens first as a finished event, and then the children laugh and wave afterwards. So perfective fits naturally:

Когда карусель остановилась... = When the carousel had stopped / stopped...

Because the laughter is presented as an ongoing action over a stretch of time, not as one completed event.

• смеяться = imperfective, to laugh
• past plural: смеялись

The phrase ещё долго strongly supports the imperfective, because it describes duration:

дети ещё долго смеялись = the children kept laughing for a long time after that

A perfective form would not sound natural here, because the point is not that they laughed once and finished, but that the laughing continued.

It is. But дети is the irregular plural of ребёнок.

• singular: ребёнок = child
• plural: дети = children

This is a very common irregular noun, and learners just need to memorize it.

Here ещё долго means something like for a long time after that, still for a long time, or continued for a long time.

• ещё often means still, yet, or more
• долго means for a long time

Together, in this context, they suggest continuation after the carousel stopped:

Когда карусель остановилась, дети ещё долго смеялись...
= When the carousel stopped, the children kept laughing for a long time afterwards...

So ещё adds the idea that the action did not stop immediately.

Because махать in the sense of to wave to someone takes the dative case for the person you are waving to.

So:

• маме = dative singular of мама
• махать кому? = to wave to whom?

Therefore:

махали маме = waved to Mom

This is different from English, where we use a preposition: wave to Mom. Russian often expresses that idea with the dative case and no preposition.

маме is the dative singular form of мама.

The noun мама is a feminine noun ending in -а, and in the dative singular that ending changes to -е:

• nominative: мама
• dative: маме

This happens because the verb махать requires the dative for the person receiving the gesture.

Because both verbs have the same subject: дети.

Russian often uses one subject followed by multiple verbs:

дети смеялись и махали
= the children laughed and waved

Since дети is plural, both past-tense verbs must also be plural:

• смеялись = they laughed / were laughing
• махали = they waved / were waving

Yes, Russian word order is flexible. This sentence uses a very natural neutral order:

Когда карусель остановилась, дети ещё долго смеялись и махали маме.

But other orders are possible, for example:

• Когда карусель остановилась, дети ещё долго маме махали и смеялись.
• Дети ещё долго смеялись и маме махали, когда карусель остановилась.

These alternatives may sound more marked or place emphasis differently. In the original sentence, маме at the end sounds smooth and natural, with no special emphasis.

Yes. Russian often leaves out possessive words like their when the meaning is obvious from context.

So махали маме most naturally means:

• waved to their mother
• or simply waved to Mom

Russian does not need to say своей маме unless there is a reason to emphasize whose mother it is.

Then Russian would usually use an imperfective verb in the when clause.

Compare:

• Когда карусель остановилась, дети ещё долго смеялись.
  = one completed stopping event

• Когда карусель останавливалась, дети смеялись.
  = whenever the carousel was stopping / every time it stopped

So in the original sentence, остановилась suggests one specific completed moment. Imperfective would suggest repeated situations, a process, or background action.

A learner may find the stress helpful:

• когда́
• карусе́ль
• останови́лась
• де́ти
• ещё
• до́лго
• смея́лись
• маха́ли
• ма́ме

Stress is important in Russian because it is unpredictable and can affect pronunciation a lot. For example, ещё is pronounced with stress on the second syllable, and смеялись is stressed on я.