Hun kommer hjem med en tegning til sin mor.

Yes. Kommer is the present tense of at komme.

In Danish, the present tense is often used:

• for something happening now
• for habits
• for near-future situations, depending on context

So Hun kommer hjem ... can mean something like She comes home ... or She is coming home ..., depending on the situation.

Hjem means home in the sense of movement toward home.

Danish often uses hjem by itself, without a preposition:

• Hun kommer hjem = She comes home
• Jeg går hjem = I’m going home

So hjem works more like an adverb here than a regular noun phrase. That is why there is no separate word like English to.

Med means with.

Here, med en tegning tells you what she has with her when she comes home. In other words, she is bringing or carrying a drawing.

So the structure is:

• med = with
• en tegning = a drawing

Because they do two different jobs:

• med en tegning = she has a drawing with her
• til sin mor = the drawing is for her mother

So:

• med describes what accompanies her
• til shows the recipient or intended destination of the drawing

They are not redundant; each adds different information.

Because tegning is a common-gender noun in Danish, so it takes en in the singular indefinite form.

Danish nouns are usually either:

• en-words (common gender)
• et-words (neuter)

So:

• en tegning = a drawing

This is something you usually just have to learn with each noun.

Yes. Tegning is related to the verb at tegne, which means to draw.

A very common pattern in Danish is:

• verb stem + -ing → a noun

So:

• at tegne = to draw
• en tegning = a drawing

This is similar to English patterns like to build / building, though the exact meaning is not always identical.

Because sin is a reflexive possessive. It is used when the possessor is the same as the subject of the clause.

Here the subject is Hun. The mother belongs to hun, so Danish uses:

• sin mor = her own mother

This is one of the most important differences from English, because English just uses her for both meanings.

Hendes mor would normally mean someone else’s mother, not the subject’s own mother.

Compare:

• Hun kommer hjem med en tegning til sin mor.
  The drawing is for her own mother.

• Hun kommer hjem med en tegning til hendes mor.
  The drawing is for another female person’s mother.

So sin points back to the subject, while hendes points to some other female person.

Because possessive words like sin, min, din, hendes, and so on normally replace the article.

So Danish says:

• sin mor = her own mother
• not sin en mor

This is the same basic idea as in English:

• her mother
• not her a mother

No, this is very normal Danish main-clause word order.

The sentence is built like this:

• Hun = subject
• kommer = verb
• hjem = adverbial
• med en tegning = prepositional phrase
• til sin mor = prepositional phrase

So the pattern is basically:

Subject + verb + other information

That is the standard order in a simple main clause.

Yes, Danish can move parts of the sentence for emphasis, but then the verb still has to stay in second position in a main clause.

For example, you could say:

• Med en tegning til sin mor kommer hun hjem.

That sounds more marked or literary, because it emphasizes what she is bringing.

The neutral, everyday version is the original:

• Hun kommer hjem med en tegning til sin mor.

Yes, very much so.

At komme hjem is a very common combination meaning to come home. Danish uses it naturally in the same way English does.

Other similar combinations are:

• gå hjem = go home
• tage hjem = go home / head home
• køre hjem = drive home

So it is useful to learn komme hjem as a chunk.

Yes. Like other possessive words in Danish, sin changes form depending on the noun.

• sin with common-gender singular nouns
  sin mor

• sit with neuter singular nouns
  sit hus

• sine with plural nouns
  sine bøger

So in this sentence, mor is a singular common-gender noun, which is why the correct form is sin.