Fuglen flyver mellem træerne i haven.

Because fuglen is the definite form: the bird.

In Danish, definiteness is usually added as an ending to the noun instead of using a separate word like English the.

• en fugl = a bird
• fuglen = the bird

So fuglen flyver ... means the bird is flying ..., not a bird is flying ....

Træerne is the plural definite form of træ.

The forms are:

• et træ = a tree
• træer = trees
• træerne = the trees

So mellem træerne means between the trees.

This is another example of Danish putting definiteness onto the noun itself rather than using a separate word.

Because have is a common gender noun in Danish, so its definite singular ending is -n / -en, not -t / -et.

The forms are:

• en have = a garden
• haven = the garden

Compare that with a neuter noun such as:

• et hus = a house
• huset = the house

So i haven means in the garden.

Because Danish usually expresses the by adding a suffix to the noun.

In this sentence:

• fugl → fuglen = the bird
• træer → træerne = the trees
• have → haven = the garden

This is one of the biggest differences from English. Instead of the bird, Danish often says bird-the, in effect.

Flyver is the present tense of the verb at flyve = to fly.

Danish present tense is often formed with -r added to the infinitive:

• at flyve = to fly
• flyver = flies / is flying

Danish does not change the verb for different persons the way English sometimes does. So you get:

• jeg flyver = I fly / I am flying
• du flyver = you fly / you are flying
• fuglen flyver = the bird flies / is flying

It can mean either, depending on context.

Danish present tense often covers both:

• fuglen flyver = the bird flies
• fuglen flyver = the bird is flying

In this sentence, most learners will naturally understand it as is flying, because the sentence describes what the bird is doing in a particular place.

Mellem means between or sometimes among, depending on context.

Here, mellem træerne means the bird is flying in the space formed by the trees, not just next to them.

So:

• mellem træerne = between the trees / among the trees

In natural English, among the trees might sometimes sound smoother, but the Danish word is still mellem here.

They give two different pieces of location information:

• mellem træerne = where the bird is flying relative to the trees
• i haven = where the whole scene is taking place

So the structure is roughly:

• the bird is flying
• between the trees
• in the garden

English does this too: The bird is flying between the trees in the garden.

Mostly yes, in this sentence.

• Fuglen = subject
• flyver = verb
• mellem træerne i haven = adverbial/prepositional phrases

So the basic order is:

Subject + Verb + Place

That said, Danish has a strong verb-second rule in main clauses. If another element comes first, the verb still usually stays in second position. For example:

• I haven flyver fuglen mellem træerne.

That is also correct Danish, and now i haven has been moved to the front for emphasis.

Yes, that is possible, but it changes the emphasis slightly.

• mellem træerne i haven naturally groups the trees in the garden
• i haven mellem træerne sounds more like: first locating the action in the garden, then narrowing it down to between the trees

Both can work, but Fuglen flyver mellem træerne i haven is very natural.

The dictionary forms are:

• fugl = bird
• træ = tree
• have = garden
• at flyve = to fly

The sentence uses inflected forms:

• fuglen = definite singular
• træerne = definite plural
• haven = definite singular
• flyver = present tense

Learning to spot the base form inside the ending is very useful in Danish.

Many Danish nouns do have different plural patterns, so this is a good question.

For træ, the pattern is:

• et træ
• træer
• træerne

So it takes -er in the plural and -ne on top of that in the definite plural.

Yes, Danish plural formation can be unpredictable, so it is often best to learn nouns together with their article and plural form, for example:

• et træ, træer
• en have, haver
• en fugl, fugle

Yes, træerne can be tricky because it contains several vowel sounds in a row.

It is roughly something like TRAIR-neh for an English speaker, but that is only an approximation.

A few useful points:

• træ has a vowel somewhat like the a in British cat, but not exactly
• -erne is a common definite plural ending
• in normal speech, the word may sound more compressed than its spelling suggests

This is a word worth listening to from native audio, because spelling and pronunciation do not line up perfectly.

Sometimes yes, but mellem is the most straightforward choice here.

Both mellem and imellem can relate to the idea of between, but mellem is the standard preposition in a sentence like this:

• Fuglen flyver mellem træerne.

For a learner, mellem is the form to remember first.

Because of the definite forms, it normally sounds like a specific scene:

• fuglen = the bird
• træerne = the trees
• haven = the garden

So it feels like speaker and listener can identify them from context.

If you wanted a more general statement, you might use indefinite forms, depending on the meaning:

• En fugl flyver mellem træer i en have.

But that sounds much less natural as a normal descriptive sentence, because it is vague and less grounded in a particular situation.