Hvis koncerten er gratis igen i næste uge, tager min søster gerne med, og så føler hun sig heldig.

Because koncerten means the concert.

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

• en koncert = a concert
• koncerten = the concert

So Hvis koncerten er gratis igen ... is If the concert is free again ...

Hvis means if and introduces a condition.

So the first part:

• Hvis koncerten er gratis igen i næste uge
  = If the concert is free again next week

This is a conditional clause, and it sets up the situation for what happens next.

This is because Danish uses verb-second word order in main clauses.

The sentence begins with the if-clause:

• Hvis koncerten er gratis igen i næste uge

After that whole clause, the main clause starts. In a Danish main clause, the finite verb usually comes in second position, so you get:

• tager min søster gerne med

not

• min søster tager gerne med

This is very common in Danish after fronted elements such as:

• time expressions
• subordinate clauses
• adverbs

Compare:

• Min søster tager gerne med.
• I næste uge tager min søster gerne med.
• Hvis koncerten er gratis, tager min søster gerne med.

Gerne often means something like gladly, willingly, or with pleasure.

So:

• min søster tager gerne med

means that the sister is happy or willing to come along.

It does not literally mean likes by itself, but in some contexts it can feel similar:

• Jeg drikker gerne kaffe = I like drinking coffee / I gladly drink coffee
• Hun tager gerne med = She is happy to come along

Because tage med is a verb expression meaning to come along / to take along / to join depending on context.

In Danish, particles like med, op, ud, ind are often separated from the verb in main clauses.

So:

• Hun tager med = She comes along
• infinitive: at tage med

This is similar to separable phrasal verbs in English, although the grammar is not exactly the same.

Here tage med means come along or join.

So:

• min søster tager gerne med

means that the sister is willing to go too.

Depending on context, tage med can also mean take something/someone along, but here the subject is the person joining the event, so come along is the most natural understanding.

Igen means again, and in this sentence it modifies the idea of the concert being free another time.

• er gratis igen = is free again

This word order is natural in Danish. The sentence is focusing on the state gratis first, then adding igen.

You may also hear slightly different placements in other contexts, but er gratis igen is completely normal and idiomatic.

Danish often uses time expressions without an article in cases like this.

• i næste uge = next week
• i morgen = tomorrow
• sidste år = last year

So næste uge does not need en or den here.

Compare:

• næste uge = next week
• den næste uge would usually mean the next week in a more specific, less common sense

Here så means something like then, so, or in that case.

The phrase:

• og så føler hun sig heldig

adds a result or next step:

• and then she feels lucky
• and so she feels lucky

It helps connect the ideas smoothly.

Because Danish uses the reflexive pronoun sig when the subject and object refer to the same person.

Here the subject is hun = she, and she is the one who feels herself lucky.

So:

• hun føler sig heldig = she feels lucky

The reflexive pronoun for third person is:

• sig

Compare:

• Jeg føler mig heldig = I feel lucky
• Du føler dig heldig = You feel lucky
• Hun føler sig heldig = She feels lucky

You would not use hende here, because hende is a normal object pronoun, not a reflexive one.

Because heldig is describing the subject after føle sig.

In Danish, after verbs like være, blive, føle sig, you often use an adjective as a subject complement:

• Hun er glad = She is happy
• Hun føler sig heldig = She feels lucky

So heldig is not modifying the verb; it is describing hun.

Together, og så often means and then, and so, or and in that case.

In this sentence it links the second idea naturally to the first one:

• ..., og så føler hun sig heldig.

This can suggest sequence, consequence, or a natural follow-up.

The comma after the if-clause separates the subordinate clause from the main clause:

• Hvis koncerten er gratis igen i næste uge, tager min søster gerne med ...

That comma is very helpful because it marks the end of the condition and the start of the main statement.

There is also a comma before og in your example. In Danish, comma usage can vary somewhat depending on whether someone follows traditional comma or new comma conventions, but many learners will see commas used this way in real texts.

Yes. You could rearrange it, but the word order would change.

For example:

• Min søster tager gerne med, hvis koncerten er gratis igen i næste uge.

That is also correct.

When the main clause comes first, it has normal word order:

• Min søster tager ...

When the if-clause comes first, the main clause shows inversion:

• Hvis ..., tager min søster ...

So the meaning stays similar, but the sentence structure changes.