Min datter tager mig i hånden, når vi går over vejen.

Because datter is a common-gender singular noun in Danish: en datter.

The possessive forms are:

• min = for common-gender singular nouns
• mit = for neuter singular nouns
• mine = for plural nouns

So:

• min datter = my daughter
• mit barn = my child
• mine børn = my children

After a possessive like min, Danish normally does not use a separate article.

So you say:

• min datter = my daughter

not:

• min datteren
• den min datter

This works much like English: my daughter, not my the daughter.

Because mig is the object form of the pronoun, while jeg is the subject form.

In this sentence:

• Min datter = the subject
• tager = the verb
• mig = the object

So:

• jeg = I
• mig = me

Compare:

• Jeg går over vejen. = I cross the road.
• Min datter tager mig i hånden. = My daughter takes me by the hand.

Literally, it means takes me in the hand.

But in natural English, this is usually:

• takes me by the hand
• holds my hand

In Danish, this is a very normal way to express the idea of physically taking someone’s hand, especially to guide or protect them.

This is a very common Danish pattern with body parts.

Instead of using a possessive every time, Danish often uses:

person + preposition + definite body part

So:

• tager mig i hånden = takes me by the hand
• ser mig i øjnene = looks me in the eyes
• slår ham på armen = hits him on the arm

To an English speaker, my hand may feel more natural, but Danish often prefers the definite form when it is already obvious whose body part is meant.

Because hånden is the definite singular form of hånd.

• en hånd = a hand
• hånden = the hand

In the expression tage nogen i hånden, the definite form is the normal one.

So:

• tage mig i hånden
• not usually tage mig i hånd

Because når is used for something that happens regularly, generally, or in the future.

Here the meaning is something like:

• when/whenever we cross the road

That sounds like a repeated or usual situation, so når fits.

Use da for one specific event in the past:

• Da vi gik over vejen, tog hun mig i hånden. = When we crossed the road, she took me by the hand.

So:

• når = when/whenever, in general or in the future
• da = when, for a specific past occasion

Because Danish often uses the present tense for things that are habitual or generally true.

So når vi går over vejen means something like:

• when we cross the road
• when we are crossing the road
• whenever we cross the road

English sometimes chooses between cross, are crossing, or go across, but Danish often just uses the simple present: går.

That is just the normal Danish way to express it.

Literally:

• går = walk/go
• over = over/across
• vejen = the road

So går over vejen means go across the road / cross the road.

This is one of those places where Danish and English divide up the idea a little differently. English often uses the single verb cross, while Danish commonly uses gå over.

Because vejen is the definite form:

• en vej = a road
• vejen = the road

In this sentence, it means the road, so the definite form is needed.

Because når introduces a subordinate clause, and subordinate clauses normally keep the order:

subject + verb

So:

• når vi går over vejen = when we cross the road

not:

• når går vi over vejen

The version går vi would be the kind of inversion you expect in a main clause or question, for example:

• Går vi over vejen? = Are we crossing the road?

Yes. If the subordinate clause comes first, the main clause usually has inversion.

So you can say:

• Min datter tager mig i hånden, når vi går over vejen.

But also:

• Når vi går over vejen, tager min datter mig i hånden.

Notice that in the second version, the verb tager comes before the subject min datter in the main clause. That is normal Danish word order after an opening clause.

Because når vi går over vejen is a subordinate clause.

In Danish, many writers place a comma before a subordinate clause like this:

• Min datter tager mig i hånden, når vi går over vejen.

You may also see Danish written without that comma, depending on the comma system being used. So the comma here is very normal, but punctuation practice can vary a bit.

Yes, a few:

• datter: the a is not like English date; it is shorter and flatter.
• tager: the g is soft, not a hard English g.
• hånden: å sounds roughly like the vowel in awe; the d is soft.
• vejen: often pronounced something like VY-en or VAI-en, depending on accent and speech style, with a very light ending.

Also, Danish pronunciation is often less phonetic than spelling suggests, so it helps to hear the whole sentence spoken aloud a few times.