Min bedstemor giver mig et varmt kram, når jeg kommer på besøg.

Because Danish, like German, very often forms compound nouns as a single word.

So bedstemor is literally made from:

• bedste = best
• mor = mother

But together, bedstemor means grandmother.

This is very normal in Danish. A few similar examples are:

• bedstefar = grandfather
• fødselsdag = birthday
• sommerferie = summer holiday

English often uses two words where Danish uses one.

Because bedstemor is a common-gender noun in Danish.

Danish singular nouns have two grammatical genders:

• common gender → takes en, min
• neuter → takes et, mit

Since the noun is en bedstemor, the correct possessive is min:

• min bedstemor = my grandmother

Compare:

• min bog = my book
• mit hus = my house

So the form of my depends on the gender of the noun.

Because Danish does not use an article together with a possessive in this kind of phrase.

So you say:

• min bedstemor

not:

• en min bedstemor
• min en bedstemor

This works the same way as in English: you say my grandmother, not a my grandmother.

Giver is the present tense of give.

The verb forms are:

• infinitive: at give = to give
• present: giver = gives / is giving
• past: gav = gave
• past participle: givet = given

In Danish, the present tense very often ends in -r.

Here, giver is used because the sentence describes something that happens regularly or habitually:

• Min bedstemor giver mig et varmt kram = My grandmother gives me a warm hug

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

• jeg = I
• mig = me

In this sentence:

• Min bedstemor is the subject
• giver is the verb
• mig is the person receiving something

So Danish works like English here:

• Jeg giver hende en bog = I give her a book
• Hun giver mig en bog = She gives me a book

You use jeg when the pronoun is doing the action, and mig when the action is done to/for that person.

Because kram is a neuter noun, so it takes:

• the article et
• the adjective ending -t in the singular indefinite form

That gives:

• et kram = a hug
• et varmt kram = a warm hug

The adjective varm changes to varmt because it agrees with a neuter singular noun.

Compare:

• en varm kop = a warm cup
• et varmt kram = a warm hug

So there are two things happening:

1. kram is neuter, so you use et
2. the adjective matches that neuter noun, so varm becomes varmt

Yes. That is also correct, but it is a little different in style.

• Min bedstemor giver mig et varmt kram = My grandmother gives me a warm hug
• Min bedstemor krammer mig = My grandmother hugs me

The version with giver ... et kram is very natural and slightly more descriptive. It often feels a bit warmer or more specific, especially with an adjective like varmt.

So both are good Danish, but they are not exactly identical in tone.

Because når is used for when in situations that are repeated, habitual, or expected.

In this sentence, the meaning is something like whenever I come to visit or when I come to visit as a usual thing. That is why når fits well.

A useful contrast is:

• når = when / whenever, for repeated or expected situations
• da = when, for a single event in the past
• hvis = if

Examples:

• Når jeg kommer på besøg, får jeg kaffe. = When/Whenever I come to visit, I get coffee.
• Da jeg kom på besøg i går, fik jeg kaffe. = When I came to visit yesterday, I got coffee.
• Hvis jeg kommer på besøg, ringer jeg først. = If I come to visit, I call first.

Because når introduces a subordinate clause, and subordinate clauses normally keep the order subject + verb.

So:

• når jeg kommer på besøg

has the normal subordinate-clause order:

• når
  • jeg
    • kommer

This is different from main clauses, where Danish often follows the verb-second pattern.

Compare:

• main clause: Jeg kommer på besøg.
• subordinate clause: når jeg kommer på besøg

If the subordinate clause comes first, then the main clause shows inversion:

• Når jeg kommer på besøg, giver min bedstemor mig et varmt kram.

Notice how giver comes before min bedstemor in that version.

Because Danish often uses the present tense after words like når, even when the meaning is future.

So Danish prefers:

• Når jeg kommer på besøg i morgen ...

rather than something like:

• Når jeg vil komme ... in this meaning

This is similar to English, which also often uses the present after when:

• When I come tomorrow ...

not usually:

• When I will come tomorrow ...

So når jeg kommer is the normal Danish pattern.

På besøg is a fixed expression meaning visiting or on a visit.

So:

• komme på besøg = to come to visit
• være på besøg = to be visiting / to be on a visit

The preposition på is just part of the expression. It does not translate neatly word-for-word here, so it is best learned as a chunk:

• komme på besøg

You can also compare:

• Jeg kommer på besøg hos min bedstemor. = I come to visit my grandmother.
• Jeg er på besøg hos min bedstemor. = I am visiting my grandmother.

Because når jeg kommer på besøg is a subordinate clause, and Danish often places a comma before such clauses.

So the comma marks the boundary between:

• main clause: Min bedstemor giver mig et varmt kram
• subordinate clause: når jeg kommer på besøg

You may also see Danish written without that comma, depending on the comma system being used. But with a comma here is very common and completely normal.

So the comma is helping show the sentence structure.