Nahoře je velká skříň a dole u dveří jsou jen boty a kabáty.

Because the verb být (to be) agrees with what follows:

• je = is for singular
• jsou = are for plural

So:

• Nahoře je velká skříň = upstairs there is a big wardrobe
• dole u dveří jsou jen boty a kabáty = downstairs/by the door there are only shoes and coats

The subject in the first part is skříň (singular), and in the second part it is boty a kabáty (plural).

Because the adjective has to agree with the noun it describes.

Skříň is:

• feminine
• singular
• nominative here

So velký (big) changes to velká to match it.

A few basic forms are:

• velký stůl = a big table (masculine)
• velká skříň = a big wardrobe (feminine)
• velké okno = a big window (neuter)

This is called adjective agreement.

They are adverbs.

They describe location:

• nahoře = up / upstairs / above
• dole = down / downstairs / below

In this sentence they answer the question where?

• Nahoře je velká skříň.
• Dole u dveří jsou jen boty a kabáty.

They do not change form for gender, number, or case.

This is a very common question.

• nahoře, dole = location (where?)
• nahoru, dolů = direction/movement (where to?)

So:

• Nahoře je skříň. = The wardrobe is upstairs.
  (location)
• Jdu nahoru. = I am going upstairs.
  (movement)

And:

• Boty jsou dole. = The shoes are downstairs.
  (location)
• Jdu dolů. = I am going downstairs.
  (movement)

In your sentence, no one is moving, so nahoře and dole are correct.

After the preposition u (by, near, at), Czech uses the genitive case.

So:

• u + genitive

The basic form is dveře (door), but after u it becomes dveří:

• u dveří = by the door / near the door

This is one of the most important things to learn with Czech prepositions: each preposition typically requires a specific case.

Because dveře is a noun that is normally used only in the plural in Czech, even when English uses singular door.

This type of noun is sometimes called plural-only in practical learner terms.

So:

• basic form: dveře
• genitive plural: dveří

That is why you get:

• u dveří = by the door

Other Czech nouns can work similarly, where the form does not match English singular/plural expectations.

They are in the nominative plural, because they are the things that are there.

Basic singular/plural:

• bota → boty
• kabát → kabáty

In the sentence:

• jsou boty a kabáty = there are shoes and coats

Since they are the grammatical subject of jsou, nominative plural is used.

Jen means only / just.

In this sentence:

• dole u dveří jsou jen boty a kabáty

it limits what is there: only shoes and coats.

Its position is fairly natural here because it comes right before the nouns it focuses on:

• jsou jen boty a kabáty = there are only shoes and coats

In Czech, word order is flexible, but jen is usually placed close to the word or phrase it modifies.

Czech often uses je / jsou by themselves for this kind of existential meaning.

So English says:

• There is a big wardrobe upstairs.
• There are only shoes and coats by the door.

But Czech naturally says:

• Nahoře je velká skříň.
• Dole u dveří jsou jen boty a kabáty.

Czech does not need a separate dummy subject like English there in this structure.

Yes, Czech word order is more flexible than English word order.

This sentence begins with location:

• Nahoře je velká skříň
• dole u dveří jsou jen boty a kabáty

That feels natural because it sets the scene first: where something is.

You could rearrange parts for emphasis, but the original version is very normal and natural. For example, Czech often places known/background information earlier and new/focused information later.

So this word order highlights:

1. the location first
2. the things found there second

Actually, the full second part does contain the verb:

• dole u dveří jsou jen boty a kabáty

Here dole u dveří is one larger location phrase:

• dole = down/downstairs
• u dveří = by the door

So together it means something like downstairs by the door or down below near the door.

Czech often stacks location expressions like this very naturally.

Yes, skříň is feminine, even though it ends in a consonant. That can surprise English speakers.

In Czech, many feminine nouns do end in -a, but not all of them. A group of feminine nouns ends in a soft consonant, and skříň belongs to that group.

So you simply have to learn it as:

• ta skříň = the wardrobe/cupboard

That is why the adjective is:

• velká skříň

not velký skříň.

A few helpful points:

• Czech stress is usually on the first syllable.
• ř is the famous Czech sound; it is difficult for many learners.
• ň sounds like ny in canyon.
• í is a long vowel.

So roughly:

• skříň ≈ skrzheeny without the final vowel, but this is only a rough guide
• dveří ≈ DVE-rzhee

More usefully:

• skříň = one syllable after skř-, ending with soft ň
• dveří = stress on dve-, long -ří

If pronunciation is a priority, it is best to hear a native speaker, especially for ř.

Yes. In this sentence, a is the normal coordinating conjunction and.

It connects the two parts:

• Nahoře je velká skříň
• a dole u dveří jsou jen boty a kabáty

It also connects the two nouns at the end:

• boty a kabáty = shoes and coats

So the same word a can connect clauses or individual words, just like English and.