В сентябре дети возвращаются в школу, а вечера становятся прохладнее.

Because сентябрь changes to the prepositional case after в when в means in a time expression.

• сентябрь = September
• в сентябре = in September

This is very common with months:

• в январе = in January
• в мае = in May
• в августе = in August

So в сентябре simply means in September.

Дети is the normal plural word for children. It is actually the plural of ребёнок.

• ребёнок = child
• дети = children

Russian often has irregular plural forms, and this is one of them. You should learn ребёнок → дети as a pair.

Возвращаются is the 3rd person plural present tense form of возвращаться, meaning to return / to come back.

It matches дети, which is plural:

• дети возвращаются = the children return / are returning / come back

The ending -ются tells you:

• it is plural
• it is present tense
• the verb is reflexive because of -ся

So the grammar agrees with the subject дети.

The -ся makes the verb reflexive. In many cases, it does not have to mean a literal themselves in English. With возвращаться, it is simply the normal verb meaning to return / come back.

Compare:

• возвращать = to return something
• возвращаться = to return, to come back

So here:

• дети возвращаются в школу = the children return to school

The -ся is just part of the standard verb form you need here.

Because в школу shows movement toward a place.

With в:

• в + accusative = into / to
• в + prepositional = in / inside / at

Here the children are returning to school, so Russian uses the accusative:

• школа → в школу

Compare:

• Дети идут в школу. = The children go to school.
• Дети в школе. = The children are at school.

So:

• в школу = to school
• в школе = at school / in school

А often means and, but it has a slight sense of contrast or comparison between two ideas.

Here the sentence presents two seasonal changes happening at the same time:

• children return to school
• evenings become cooler

So а works like:

• and meanwhile
• while
• whereas (very lightly)

It links the two parts while setting them side by side.
If you used и, it would sound more like a simple list of facts. А feels more natural here.

Yes. Вечера here is the nominative plural of вечер and it is the subject of the second clause.

• вечер = evening
• вечера = evenings

This is another noun with an irregular-looking plural pattern. Many masculine nouns form the plural in -а instead of -ы or -и.

Here:

• вечера становятся прохладнее = evenings become cooler

So вечера is the thing doing the becoming.

Становятся is the 3rd person plural present tense of становиться, meaning to become.

It agrees with вечера, which is plural:

• вечера становятся = evenings become

This is a very common structure in Russian:

• дни становятся короче = the days become shorter
• вода становится холоднее = the water becomes colder

So становятся is used because the subject is plural.

Прохладнее is the comparative form of прохладный, which means cool.

• прохладный = cool
• прохладнее = cooler

Russian often forms comparatives with -ее / -ей.
So:

• вечера становятся прохладнее = evenings become cooler

Notice that Russian does not need a separate word like more here. The comparative is built into the adjective form itself.

That is a great question. Short answer: comparative forms in Russian usually do not change for gender, number, or case.

So even though вечера is plural, the comparative stays the same:

• вечер прохладнее = the evening is cooler
• вечера прохладнее = the evenings are cooler

This is different from full adjectives like:

• прохладный вечер
• прохладные вечера

But the comparative прохладнее is indeclinable in normal use.

Grammatically, возвращаются is present tense. But in Russian, the present tense is often used for:

• general truths
• repeated actions
• habitual events
• things that regularly happen at a certain time

So here it means something like:

• In September, children go back to school
• In September, children return to school

It is a regular seasonal fact, not necessarily something happening at this exact second.

Yes, Russian word order is flexible. The version here is very natural because it starts with the time setting:

• В сентябре = In September

Then it gives the first event:

• дети возвращаются в школу

Then the second:

• а вечера становятся прохладнее

This order is good because it first tells you when everything happens.

Other orders are possible, for example:

• Дети в сентябре возвращаются в школу...
• В школу дети возвращаются в сентябре...

But they may shift the emphasis. The original sentence is the most neutral and natural for general description.

Yes. In natural English, both are good translations depending on context.

• return to school is a bit more literal
• go back to school is often more natural in everyday English

Russian возвращаться covers this idea of coming back to a place after an absence. So both are valid ways to understand it.

Russian does not have articles like the or a/an.

So nouns like:

• дети
• школу
• вечера

can mean:

• children / the children
• school / the school
• evenings / the evenings

The exact meaning comes from context. In this sentence, English naturally uses:

• children return to school
• evenings become cooler

Russian simply does not need articles to say that.