После уборки ковёр в гостиной снова стал чистым.

Because после requires the genitive case.

The base form is уборка (cleaning, tidying up). After после (after), it changes to уборки:

• уборка → nominative
• после уборки → genitive

This is a very common pattern in Russian:

• после работы = after work
• после урока = after the lesson
• после дождя = after the rain

So после уборки means after the cleaning or after cleaning.

Because ковёр is the subject of the sentence — it is the thing that became clean.

In Russian, the subject is normally in the nominative case. Here:

• ковёр = the carpet
• стал = became
• чистым = clean

So the basic core is:

ковёр стал чистым = the carpet became clean

That is why ковёр stays in the nominative.

Because this sentence is talking about location, not motion.

With в, Russian uses:

• prepositional for where?
• accusative for where to?

Here, the carpet is in the living room, so it is a location:

• в гостиной = in the living room

Compare:

• ковёр в гостиной = the carpet is in the living room
• нести ковёр в гостиную = to carry the carpet into the living room

So:

• в гостиной = where?
• в гостиную = to where?

Here стал means became.

The verb is стать, which often means to become when followed by a noun or adjective-like complement:

• стать врачом = to become a doctor
• стать лучше = to become better
• стать чистым = to become clean

So снова стал чистым means became clean again.

This is a very common Russian way to express a change of state.

Because Russian past tense verbs agree with the subject in gender and number.

The subject is ковёр, which is masculine singular, so the verb is:

• стал = masculine singular past

Compare:

• ковёр стал чистым = the carpet became clean
• комната стала чистой = the room became clean
• окно стало чистым = the window became clean
• ковры стали чистыми = the carpets became clean

So стал matches ковёр.

Because after стать in the sense of to become, Russian normally uses the instrumental case for the resulting state.

So:

• чистый = nominative
• чистым = instrumental masculine singular

That is why we say:

• ковёр стал чистым

and not normally ковёр стал чистый in standard Russian.

This pattern is very important:

• стал новым = became new
• стал известным = became famous
• стал спокойным = became calm

Since ковёр is masculine singular, чистым is also masculine singular instrumental.

Yes, Russian word order is fairly flexible, and снова can often move without changing the basic meaning.

Your sentence:

После уборки ковёр в гостиной снова стал чистым.

Possible alternatives:

• Ковёр в гостиной снова стал чистым после уборки.
• После уборки снова ковёр в гостиной стал чистым.
• Ковёр снова стал чистым в гостиной.

However, the original version sounds natural because it presents the information in a clear order:

1. После уборки = after cleaning
2. ковёр в гостиной = the carpet in the living room
3. снова стал чистым = became clean again

So yes, the word order can change, but the original sentence is smooth and idiomatic.

Yes — especially ковёр.

A few useful points:

• ковёр is stressed on the second syllable: ка-ВЁР
• In normal Russian writing, ё is often written as е, so you may also see ковер
• Even if written ковер, it is still pronounced ковёр

Other stress points:

• убо́рки
• гости́ной
• сно́ва
• ста́л
• чисты́м

For learners, ё is worth watching carefully because it changes pronunciation clearly.