Køletasken står ved døren og er allerede fyldt med vand og frugt.

Because køletasken is the definite form: the cooler bag / the cool bag.

In Danish, definiteness is often added as an ending:

• en køletaske = a cooler bag
• køletasken = the cooler bag

This is very common in Danish. Instead of putting a separate word like the in front, Danish usually adds -en, -et, or -ne to the noun.

Here:

• køletaske is a common-gender noun
• so the definite singular becomes køletasken

Står literally means stands, but in Danish it is very often used for the position of objects.

So:

• Køletasken står ved døren = The cooler bag is standing by the door

In natural English, we would usually just say is by the door, but Danish often prefers a position verb such as:

• stå = stand
• ligge = lie
• sidde = sit

This does not always mean the object is doing anything active. It is just the normal Danish way to describe where something is.

Yes, you can, and it would be understood.

But there is a difference in feel:

• Køletasken står ved døren sounds more natural if the bag is upright or placed there in a way Danish sees as standing
• Køletasken er ved døren simply says where it is, without that positional nuance

Danish often prefers stå / ligge / sidde where English just uses be.

Ved usually means by, near, or at.

So:

• ved døren = by the door / at the door

It tells you the cooler bag is located close to the door.

This is different from:

• i døren = in the door (not natural here)
• på døren = on the door
• foran døren = in front of the door
• ved siden af døren = next to the door

So ved is the normal choice for by the door.

For the same reason as køletasken: it is definite.

• en dør = a door
• døren = the door

So ved døren means by the door, not by a door.

Again, Danish usually marks definiteness with an ending rather than a separate word.

Er fyldt med means is filled with.

It is a very common pattern:

• er = is
• fyldt = filled
• med = with

So:

• Køletasken er fyldt med vand og frugt = The cooler bag is filled with water and fruit

You can use this pattern with many nouns:

• Glasset er fyldt med vand = The glass is filled with water
• Tasken er fyldt med bøger = The bag is filled with books

In this sentence, fyldt functions like an adjective/past participle meaning filled.

It comes from the verb at fylde = to fill.

So:

• at fylde = to fill
• fyldt = filled

In er fyldt med, it works much like English is filled with.

Allerede means already.

In this sentence:

• er allerede fyldt med ...

That placement is normal in Danish. It comes after the verb er and before the participle/adjective fyldt.

Compare:

• Den er allerede klar = It is already ready
• Han har allerede spist = He has already eaten

So the position of allerede here is very natural.

Because the subject stays the same.

The sentence is:

• Køletasken står ved døren og er allerede fyldt med vand og frugt.

The subject køletasken applies to both verbs:

• står
• er

English does the same:

• The cooler bag is by the door and is already filled with water and fruit.

You could repeat the subject, but it would usually sound unnecessary.

Because vand and frugt are being used in a general or substance sense.

• vand = water
• frugt = fruit

In English, we also often say:

• filled with water and fruit

not necessarily:

• filled with the water and the fruit

So Danish does not need articles here.

If you meant specific items, the wording could change depending on context.

Grammatically, frugt is singular in form, but it often works like a mass/general noun, much like English fruit.

So fyldt med vand og frugt means the bag contains:

• water
• fruit in general

If you wanted to emphasize separate pieces or kinds, Danish might use a different structure, but frugt is perfectly natural here.

The structure is:

• Køletasken = subject
• står = verb
• ved døren = location
• og = and
• er allerede fyldt med vand og frugt = second verb phrase

So the pattern is roughly:

Subject + verb + location + and + verb phrase

This follows normal Danish main-clause word order, where the finite verb comes early in the clause.

A few words in this sentence can be difficult for English speakers:

• køletasken
• døren
• fyldt

Helpful notes:

• ø in køle- and døren is a front rounded vowel that English does not really have
• y in fyldt is also a front rounded vowel
• døren often sounds softer and more reduced than learners expect
• fyldt may sound much shorter and less clearly pronounced than its spelling suggests

A rough learner-friendly guide:

• køletasken ≈ KUR-leh-tas-gen (very approximate)
• døren ≈ DUR-en with a rounded vowel
• fyldt ≈ something like fylt with rounded lips

These are only approximations. For pronunciation, it is best to listen to native audio, especially for ø, y, and soft Danish consonants.

The main nouns are:

• en køletaske = a cooler bag
• en dør = a door
• vand = water
• frugt = fruit

In the sentence, two of them appear in the definite form:

• køletasken = the cooler bag
• døren = the door

This is useful because when you look words up, you usually search for the indefinite singular form:

• køletaske
• dør