Sprzątanie kuchni po obiedzie jest ważne.

In this sentence, sprzątanie is a verbal noun, not a finite verb.

It comes from the verb sprzątać (to clean / to tidy up) and means cleaning or the act of cleaning.

So:

• sprzątać = to clean
• sprzątanie = cleaning

In Sprzątanie kuchni po obiedzie jest ważne, the whole phrase sprzątanie kuchni po obiedzie acts like the subject of the sentence: Cleaning the kitchen after dinner is important.

Because kuchni is the genitive singular form of kuchnia (kitchen).

After verbal nouns like sprzątanie, Polish often uses the thing being affected in the genitive:

• sprzątanie kuchni = cleaning of the kitchen
• not sprzątanie kuchnia

This is very common in Polish with nouns formed from verbs.

Compare:

• czytanie książki = reading a book
• mycie samochodu = washing a car
• sprzątanie kuchni = cleaning the kitchen

So even though English says cleaning the kitchen, Polish uses a structure closer to cleaning of the kitchen.

Po takes the locative case when it means after in time expressions.

So:

• obiad = dinner / lunch
• po obiedzie = after dinner / after lunch

This is why obiad changes to obiedzie.

A few similar examples:

• po pracy = after work
• po lekcji = after class
• po śniadaniu = after breakfast

So po obiedzie is just the normal required form after po.

Because the subject is sprzątanie, and sprzątanie is a neuter noun.

Polish adjectives must agree with the noun they describe:

• ważny = masculine
• ważna = feminine
• ważne = neuter

Since sprzątanie is neuter, we say:

• Sprzątanie ... jest ważne.

Even though English uses important without changing its form, Polish adjectives must match gender and number.

Yes, in standard Polish, jest is normally used here.

The sentence structure is:

• Sprzątanie kuchni po obiedzie = subject
• jest = is
• ważne = important

So the full sentence is natural and correct:

• Sprzątanie kuchni po obiedzie jest ważne.

If you remove jest, the sentence sounds incomplete in normal standard Polish.

Yes, Polish word order is fairly flexible, though some orders sound more natural than others depending on emphasis.

The neutral order is:

• Sprzątanie kuchni po obiedzie jest ważne.

But you could also say:

• Po obiedzie sprzątanie kuchni jest ważne.
  This emphasizes after dinner.

• Ważne jest sprzątanie kuchni po obiedzie.
  This emphasizes important.

The original version is a very natural, neutral sentence.

Because Polish has no articles like a / an / the.

So kuchnia or kuchni can mean:

• a kitchen
• the kitchen

The exact meaning depends on context.

In this sentence, sprzątanie kuchni naturally means cleaning the kitchen, even though there is no separate word for the.

No, not in this sentence.

Kuchnię is the accusative form, and that would be used after a normal verb:

• Sprzątam kuchnię. = I am cleaning the kitchen.

But here we have a noun: sprzątanie (cleaning), not the finite verb sprzątam.

With this noun, Polish normally uses the genitive:

• sprzątanie kuchni = cleaning the kitchen

So:

• Sprzątam kuchnię ✅
• Sprzątanie kuchni ✅
• Sprzątanie kuchnię ❌

This is about aspect.

• sprzątanie comes from the imperfective verb sprzątać
• posprzątanie comes from the perfective verb posprzątać

Very roughly:

• sprzątanie focuses on the activity/process of cleaning
• posprzątanie focuses more on completing the cleaning

In your sentence, sprzątanie kuchni po obiedzie jest ważne sounds natural because it talks generally about the activity or habit.

If you used posprzątanie, it would sound more like getting the kitchen cleaned / finishing the cleaning.

Not always, and this often confuses English speakers.

In Polish, obiad is the main meal of the day, but depending on family habits and region, it may line up more closely with:

• lunch
• or dinner

So po obiedzie can be translated as after lunch or after dinner, depending on context.

The grammar stays the same either way.

It can do either, depending on context.

Because Polish has no articles, sprzątanie kuchni could mean:

• cleaning the kitchen
• cleaning a kitchen
• kitchen cleaning in general

In real use, listeners usually understand from the situation. In a household context, most people would hear it as cleaning the kitchen after the meal.

You could, but the structure would change.

The original sentence is simple and natural:

• Sprzątanie kuchni po obiedzie jest ważne.
  = Cleaning the kitchen after dinner is important.

If you want to say is an important thing, you would need a noun:

• Sprzątanie kuchni po obiedzie to ważna rzecz.

That also works, but it is a little more explicit and slightly less neutral. The original version is more straightforward and idiomatic.