W przedpokoju stoi mała szafka na buty, ale dziś jest tam duży bałagan.

Because w means in, and when Polish talks about a fixed location, w usually takes the locative case.

• przedpokój = hallway / entry hall
• w przedpokoju = in the hallway

So przedpokoju is the locative singular form of przedpokój.

Polish word order is much more flexible than English word order. Starting with W przedpokoju sets the scene first, a bit like saying:

• As for the hallway...
• In the hallway...

This is very natural in Polish. The sentence could be rearranged, but this version sounds smooth and normal.

In Polish, furniture and other upright objects often stand, so stać is very natural here.

• stoi mała szafka = a small cabinet is standing there

English usually just says there is or there stands, but Polish often prefers stoi for things like:

• stół stoi przy ścianie = the table stands by the wall
• szafa stoi w kącie = the wardrobe stands in the corner

So stoi sounds more specific and idiomatic than jest here.

Because mała szafka is the subject of the verb stoi, so it must be in the nominative case.

Also, the adjective has to agree with the noun:

• szafka is feminine singular
• so the adjective is mała

Compare:

• mała szafka stoi = the small cabinet is standing
• widzę małą szafkę = I see the small cabinet

In the second example, the noun is an object, so it changes case.

Because Polish has no articles. There is no direct equivalent of English a/an or the.

So:

• mała szafka can mean a small cabinet or the small cabinet
• duży bałagan can mean a big mess or the big mess

The exact meaning depends on context.

Literally, szafka na buty means a cabinet for shoes.

In Polish, na + accusative is often used to show purpose or intended use:

• kubek na kawę = a cup for coffee
• pudełko na zabawki = a box for toys
• szafka na buty = a cabinet for shoes

Here buty is the accusative plural form, but it looks the same as the nominative plural. That is normal for this kind of noun.

Because in Polish, ale almost always takes a comma before it when it joins two clauses.

So:

• W przedpokoju stoi mała szafka na buty, ale dziś jest tam duży bałagan.

This is standard punctuation. It works much like but joining two clauses in English, though Polish is stricter about writing the comma.

Yes, the words could be rearranged, because Polish word order is flexible. But this order highlights dziś = today.

• ale dziś jest tam duży bałagan = but today there is a big mess there

Placing dziś early makes the contrast stronger: normally the hallway may be fine, but today it is messy.

tam means there, referring back to the hallway.

Because duży bałagan is the thing that is there, so Polish uses the nominative here.

• jest tam duży bałagan = there is a big mess there

The adjective agrees with the noun:

• bałagan is masculine singular
• so the adjective is duży

A learner may expect genitive because Polish sometimes uses it in existence expressions, especially with negation:

• nie ma tam bałaganu = there is no mess there

But in this affirmative sentence, duży bałagan in the nominative is the normal form.

Yes, that is grammatical. It would mean roughly the same thing.

The difference is mainly nuance:

• stoi mała szafka sounds more physical and visual: the cabinet is standing there
• jest mała szafka is more neutral: there is a small cabinet there

So stoi is usually the more natural choice when talking about the position of a piece of furniture.