Om hun så har travlt, tager hun stadig hamsteren ud af buret og holder øje med dens pote.

Here, om ... så has a concessive meaning: it means something like even if, whether or not, or no matter if.

So:

• Om hun så har travlt ≈ Even if she is busy
• It suggests that the rest of the sentence is true despite that fact.

The word så adds emphasis. It makes the phrase stronger than plain om hun har travlt.

No. Even though om often means if/whether and can introduce indirect questions, this is not a question.

In this sentence, om is part of the pattern om ... så, which is used to mean even if / whether or not.

So this is a subordinate clause expressing contrast, not a question.

This is because Danish follows the V2 rule in main clauses: the finite verb normally comes in second position.

The whole first part, Om hun så har travlt, counts as the first element of the sentence. So in the main clause, the finite verb tager must come next:

• Om hun så har travlt, tager hun stadig ...

If you did not put that first clause at the front, the normal order would be:

• Hun tager stadig hamsteren ud af buret ...

So the inversion happens because something else has been placed first.

Have travlt is a very common fixed expression meaning to be busy or to be rushed.

So:

• Hun har travlt = She is busy

Even though the adjective is basically travl, the idiomatic expression is have travlt. Learners usually just memorize it as a set phrase.

Compare:

• Hun er travl = possible, but less idiomatic in many everyday contexts
• Hun har travlt = the usual way to say she is busy

So in this sentence, har travlt is the natural choice.

Stadig here means still.

So:

• tager hun stadig hamsteren ud af buret = she still takes the hamster out of the cage

Its position is normal Danish word order. After inversion, the order is:

• finite verb: tager
• subject: hun
• adverb: stadig

Without the fronted clause, it would be:

• Hun tager stadig hamsteren ud af buret

So stadig is not in a strange place; it is just following normal Danish sentence structure.

In Danish, the definite article is usually added to the end of the noun.

So:

• en hamster = a hamster
• hamsteren = the hamster

and

• et bur = a cage
• buret = the cage

The endings change depending on the gender of the noun:

• common gender often takes -en
• neuter often takes -et

That is why you see hamsteren and buret.

It means takes the hamster out of the cage.

The pattern is:

• tage noget ud af noget = take something out of something

So:

• tager hamsteren ud af buret
  • tager = takes
  • hamsteren = the hamster
  • ud af = out of
  • buret = the cage

This is a very common structure in Danish.

Holde øje med is a fixed expression meaning:

• keep an eye on
• watch
• monitor

So:

• holder øje med dens pote = keeps an eye on its paw

You should learn it as a set phrase:

• holde øje med nogen/noget

The word med is just part of the idiom. It does not match English word-for-word, so it is best not to translate it too literally.

Also, the singular øje is normal in this expression.

Because sin/sit/sine refers back to the subject of the clause.

Here, the subject is hun. So if you said sin pote, it would mean her own paw, which does not make sense.

But the paw belongs to hamsteren, not to hun, so Danish uses dens:

• dens pote = its paw

So:

• sin pote = her own paw
• dens pote = the hamster’s paw / its paw

That is why dens is correct here.

Because a possessive already makes the noun definite.

In Danish, when you use a possessive like:

• min
• din
• hans
• hendes
• dens

the noun normally does not take the definite ending as well.

So:

• dens pote = its paw
• not dens poten

This is similar to English: we say its paw, not its the paw.

Yes, and in many contexts that would be a very natural alternative.

• Selvom hun har travlt = Although/Even though she is busy
• Om hun så har travlt = Even if she is busy / whether or not she is busy

The difference is mainly in nuance:

• selvom is the more straightforward, common way to say although/even though
• om ... så sounds more emphatic and concessive, as if the speaker is saying: busy or not, she still does it

So both can work, but om hun så har travlt has a stronger “no matter what” feeling.