U mnie w domu jest często dużo kurzu, dlatego ścierka i mop są zawsze blisko.

Both are possible, but they feel a little different.

• W moim domu = in my house/home
• U mnie w domu literally means something like at my place, in my home

U mnie is a very common Polish way to mean at my place or where I live. Adding w domu makes it a bit more explicit: at my place, at home.

So:

• U mnie w domu jest często dużo kurzu sounds natural and conversational.
• W moim domu często jest dużo kurzu is also correct, but a bit more neutral or direct.

A learner should get used to u mnie, because Polish uses it very often in everyday speech:

• U mnie jest zimno. = It’s cold at my place.
• Byłeś kiedyś u mnie? = Have you ever been to my place?

It is genitive.

The preposition u requires the genitive case, so:

• ja → mnie
• ty → ciebie
• on → niego
• ona → niej

Examples:

• u mnie = at my place
• u ciebie = at your place
• u niego = at his place
• u niej = at her place

So u mnie is not random—it is the normal form required after u.

Because the real grammatical subject here is dużo kurzu = a lot of dust, and Polish treats this kind of quantity expression as singular/neuter in sentences like this.

So you say:

• Jest dużo kurzu. = There is a lot of dust.
• Było dużo kurzu. = There was a lot of dust.

Even though dust may feel like a large amount, grammatically dużo behaves like a singular quantity word here.

Later in the sentence, you have ścierka i mop as the subject, and that is a plural pair of things, so:

• ścierka i mop są = the cloth and the mop are

That is why the sentence has both:

• jest for dużo kurzu
• są for ścierka i mop

Because dużo requires the genitive.

The basic nominative form is:

• kurz = dust

But after quantity words such as:

• dużo = a lot of
• mało = little, not much
• trochę = a bit of
• ile = how much/how many

you usually use the genitive:

• dużo kurzu = a lot of dust
• mało czasu = little time
• trochę wody = a bit of water

So:

• nominative: kurz
• genitive: kurzu

Często means often, and here it modifies the whole situation there is a lot of dust.

So the idea is:

• jest często dużo kurzu = there is often a lot of dust

It does not mean that the dust itself is frequent in some strange way; it means the situation happens often.

Polish word order is flexible, so you may also hear:

• U mnie w domu często jest dużo kurzu.

That version is probably even easier for an English speaker to process, because często comes before the whole predicate more clearly.

Both are natural.

Dlatego means therefore, that’s why, or for that reason.

It connects a cause and a result:

• Jest dużo kurzu, dlatego ścierka i mop są zawsze blisko. = There is a lot of dust, therefore / that’s why the cloth and mop are always nearby.

It is very common in everyday Polish.

A few similar connectors:

• dlatego = therefore / that’s why
• więc = so
• z tego powodu = for this reason

Dlatego often sounds a bit more explicit than więc.

Because ścierka i mop is a compound subject made of two things:

• ścierka = cloth
• mop = mop

When two singular nouns are joined by i (and), the verb is normally plural:

• Kot i pies są w domu. = The cat and the dog are at home.
• Ścierka i mop są zawsze blisko. = The cloth and the mop are always close by.

So even though each noun is singular on its own, together they require są.

Ścierka usually means a cloth, dishcloth, cleaning cloth, or rag, depending on context.

In this sentence, because there is a lot of dust, ścierka is best understood as a cleaning cloth / duster cloth.

It comes from the verb ścierać, which can mean things like:

• to wipe off
• to rub off
• to remove by wiping

So ścierka is basically something used for wiping or cleaning.

Blisko here means nearby, close, or close at hand.

It is functioning as a predicative adverb-like word, not as a normal adjective describing a noun directly.

So:

• Ścierka i mop są zawsze blisko. = The cloth and the mop are always nearby.

If you wanted an adjective, you would need a noun to modify:

• bliski sklep = a nearby shop

But in this sentence, we are saying where the items are, not describing them as a type of object. So blisko is the natural choice.

Also, there is no specific reference point stated after it. If you wanted one, you could say:

• blisko mnie = close to me
• blisko drzwi = close to the door

But here blisko alone means close by / within reach.

Not exactly a fixed idiom, but it is a very natural combination.

• zawsze = always
• blisko = nearby / close

Together:

• zawsze blisko = always nearby / always close at hand

It suggests something is kept conveniently near because it is needed often.

So in this sentence, the idea is: because there is often a lot of dust, the cleaning tools are always kept nearby.

Yes. Polish word order is flexible, and several versions would be correct.

For example:

• U mnie w domu jest często dużo kurzu, dlatego ścierka i mop są zawsze blisko.
• U mnie w domu często jest dużo kurzu, dlatego ścierka i mop są zawsze blisko.
• Często jest u mnie w domu dużo kurzu, dlatego ścierka i mop są zawsze blisko.

These do not all sound equally natural in every context, but they are grammatically possible.

The most neutral everyday options are probably:

• U mnie w domu często jest dużo kurzu...
• U mnie w domu jest często dużo kurzu...

Polish often moves words around to shift emphasis, rhythm, or topic.

Because Polish has no articles.

English uses:

• a
• an
• the

Polish does not.

So:

• kurz can mean dust or the dust, depending on context
• ścierka can mean a cloth or the cloth
• mop can mean a mop or the mop

In this sentence, English would probably naturally translate them with the:

• the cloth and the mop are always nearby

But Polish does not need separate words for that.

Normally, no. In this meaning, kurz is a mass noun, like dust in English.

You usually talk about it as an uncountable substance:

• dużo kurzu = a lot of dust

You would not normally use a plural form to mean ordinary household dust.

So Polish treats it much like English does:

• dust is usually uncountable
• kurz is usually uncountable

It is neutral, natural everyday Polish.

Nothing in it is especially formal, but it is not slang either. A native speaker could easily say this in conversation.

A few parts make it sound especially natural and spoken:

• U mnie = at my place
• dlatego = that’s why / therefore
• zawsze blisko = always nearby

So it works well in normal speech and also in informal writing.