Min søster har en lille baby, som ofte smiler, når hun ser mig.

Because Danish normally does not use the definite ending when a possessive already makes the noun definite.

So:

• min søster = my sister
• vores hus = our house

Using søsteren here would be like saying my the sister in English. The possessive min already does the job.

Baby is a common-gender noun in Danish, so it takes en:

• en baby
• babyen = the baby

That is why the sentence says en lille baby.

A useful comparison:

• en baby
• et barn = a child

So even though both can refer to a child, they belong to different grammatical genders.

Lille means small/little, and it agrees naturally with the singular noun here.

In this sentence:

• en lille baby = a small/little baby

A few useful comparisons:

• en lille baby = common gender singular
• et lille barn = neuter singular
• små babyer = plural

Also, lille is very common with babies and children and can sound affectionate, not just physically descriptive.

Here som introduces a relative clause and refers back to baby.

So:

• en lille baby, som ofte smiler
  = a little baby, who/that often smiles

In English, this is where you would usually use who or that.

In Danish, som is a very common way to connect a noun to extra information about it.

Because som ofte smiler is a subordinate clause, and Danish word order changes in subordinate clauses.

In a main clause, you would normally say:

• Babyen smiler ofte. = The baby often smiles.

But in a subordinate clause, the adverb typically comes before the finite verb:

• ... som ofte smiler = ... who often smiles

This is a very important Danish pattern:

• main clause: verb usually comes early
• subordinate clause: adverb often comes before the verb

Når is used for when in a general, repeated, or habitual sense.

That fits this sentence because the idea is something like:

• whenever she sees me
• when she sees me, she often smiles

So når is the natural choice.

By contrast, da is usually used for a specific past occasion:

• Da hun så mig, smilede hun.
  = When she saw me, she smiled.

So:

• når = repeated/general when
• da = one specific past when

Yes, it can be ambiguous.

Grammatically, hun could refer to:

• the baby — if the baby is female
• the sister

In real life, context usually makes it clear. But if the context does not help, a Danish speaker might repeat the noun to avoid confusion:

• ..., når babyen ser mig
• ..., når min søster ser mig

So this is a good example of how Danish, like English, sometimes leaves pronoun reference a little unclear.

Because mig is the object form of jeg.

In Danish:

• jeg = I
• mig = me

Since mig is the object of ser, it must be mig:

• hun ser mig = she sees me

Compare:

• jeg ser hende = I see her
• hun ser mig = she sees me

So the same subject/object distinction exists here as in English.

The commas mark subordinate clauses.

The sentence has two of them:

• som ofte smiler — a relative clause
• når hun ser mig — a time clause

So the commas help show the structure:

• Min søster har en lille baby, som ofte smiler, når hun ser mig.

You may also see Danish written without these opening commas, depending on comma style, but the version here is completely standard and clearly shows the clause boundaries.

It sounds perfectly natural.

In Danish, lille with babies, children, animals, and family members is very common. It can mean:

• literally small
• young
• affectionate or warm in tone

So en lille baby does not sound strange. It is much like English a little baby, which is also very natural even though babies are obviously small.