Selvom hun halter, vil hun gerne tilbage på arbejde på mandag, bare hævelsen bliver mindre.

Because Danish main clauses normally follow the verb-second rule. The opening clause Selvom hun halter takes the first position in the sentence, so in the main clause the finite verb comes next:

• Selvom hun halter, vil hun ...

If the sentence started directly with the main clause, it would be:

• Hun vil gerne tilbage på arbejde på mandag ...

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

Selvom means although / even though and introduces a subordinate clause.

In Danish subordinate clauses, the word order is different from normal main-clause word order. That is why you get:

• selvom hun halter

and not a main-clause pattern like selvom halter hun.

So selvom is both giving the meaning of concession and signaling subordinate-clause word order.

Halter is the present tense of at halte, which means to limp.

So:

• at halte = to limp
• hun halter = she is limping / she limps

In this sentence, the present tense sounds natural because it describes her current condition.

Vil and gerne together often express something like wants to / would like to.

• vil on its own can mean wants to or sometimes will
• gerne adds the idea of willingness or desire

So vil hun gerne tilbage på arbejde is a natural way to say that she would like to go back to work.

It is often softer and more idiomatic than using vil alone.

Because på arbejde is a fixed expression meaning at work / to work in many contexts.

So:

• være på arbejde = be at work
• tage på arbejde = go to work
• tilbage på arbejde = back to work

The preposition på is simply part of the normal Danish expression here.

På mandag means on Monday or very often this coming Monday / next Monday, depending on context.

Danish commonly uses på with days in this kind of time expression:

• på mandag = on Monday
• på tirsdag = on Tuesday

So this is a normal idiomatic way to talk about a specific upcoming day.

Here bare means something like as long as, provided that, or if only.

So in this sentence it introduces a condition:

• bare hævelsen bliver mindre = as long as the swelling goes down / provided the swelling gets smaller

This is a very common use of bare in spoken and written Danish. It often has nothing to do with only.

Hævelsen is the definite form, meaning the swelling.

Danish often uses the definite form when the thing is already known from the situation or context. Here, the listener is expected to know which swelling is meant, probably from an injury that has already been mentioned or is obvious.

So:

• en hævelse = a swelling
• hævelsen = the swelling

Bliver mindre means gets smaller / becomes smaller, so it focuses on change.

• er mindre = is smaller
• bliver mindre = becomes / gets smaller

In this sentence, the idea is not just that the swelling is small, but that it needs to reduce. That is why bliver is the natural choice.

Yes. Mindre is the comparative form of lille or small in this context, so it means smaller.

After verbs like blive, Danish often uses a comparative adjective when talking about a change:

• bliver bedre = gets better
• bliver værre = gets worse
• bliver mindre = gets smaller

So this is a very standard pattern.

The commas separate the main clause from the subordinate clauses.

• Selvom hun halter, ...
• ..., bare hævelsen bliver mindre.

Both Selvom hun halter and bare hævelsen bliver mindre are dependent clauses attached to the main clause.

So the commas help show the structure of the sentence clearly.