Die Zugabe kommt nach dem Auftritt des Headliners.

Because nach is a preposition that always takes the dative case when it means after.

• der Auftritt = nominative
• dem Auftritt = dative

So:

• nach dem Auftritt = after the performance/appearance

You should learn nach together with dative:

• nach dem Essen = after the meal
• nach der Show = after the show
• nach dem Konzert = after the concert

That is the genitive case, which here shows possession or belonging: the performance of the headliner / the headliner’s performance.

So the structure is:

• der Auftritt = the performance
• des Headliners = of the headliner

Together:

• der Auftritt des Headliners = the headliner’s performance

For a masculine noun like der Headliner, the genitive singular is usually:

• des + noun + -(e)s

So:

• der Headliner
• des Headliners

Here is the full breakdown:

• Die Zugabe → nominative
  It is the subject of the sentence.

• kommt → the verb

• nach dem Auftritt des Headliners → a prepositional phrase

  • dem Auftritt is dative because of nach
  • des Headliners is genitive because it depends on Auftritt

So the sentence contains:

• nominative: die Zugabe
• dative: dem Auftritt
• genitive: des Headliners

Good question. In German, kommen can also be used in a broader sense like to come on, to happen next, or to take place later in the sequence.

So here Die Zugabe kommt nach ... means something like:

• The encore comes after ...
• The encore happens after ...
• The encore is after ...

It is not necessarily about movement from one place to another. It is about order in time or sequence.

Because it is the subject, and German main clauses normally place the finite verb in second position.

The pattern here is:

• Die Zugabe = first element
• kommt = second element
• nach dem Auftritt des Headliners = the rest

This is a normal German main clause pattern:

• Der Film beginnt um acht.
• Das Konzert endet spät.
• Die Zugabe kommt nach dem Auftritt des Headliners.

You could also move another element to the front, but then the verb still stays second:

• Nach dem Auftritt des Headliners kommt die Zugabe.

That version is also correct.

Yes, Headliner is a loanword from English, but German treats it like a normal noun and gives it a grammatical gender. In this sentence it is masculine:

• der Headliner
• dem Headliner
• des Headliners

German often assigns gender to borrowed nouns, and then they decline like other German nouns.

Auftritt usually means an appearance, performance, or stage appearance, depending on context.

In entertainment contexts, it often means:

• a performer’s appearance on stage
• a set or performance

So der Auftritt des Headliners is the headliner’s performance or stage appearance.

It comes from the verb auftreten, which can mean to appear or to perform.

Yes, you may hear that in everyday spoken German, especially in more colloquial speech.

• nach dem Auftritt des Headliners = more standard, more elegant written German
• nach dem Auftritt vom Headliner = more colloquial spoken German

The sentence you were given uses the genitive, which is usually the better choice in formal or neutral written German.

Because many masculine and neuter nouns in German do not add a visible noun ending in the dative singular. The article shows the case clearly:

• der Auftritt → nominative
• dem Auftritt → dative

The noun itself stays the same here.

Compare:

• der Tag → dem Tag
• der Film → dem Film
• der Auftritt → dem Auftritt

So the case is mainly marked by dem, not by changing Auftritt.

Yes, absolutely. That is a very natural alternative.

Both are correct:

• Die Zugabe kommt nach dem Auftritt des Headliners.
• Nach dem Auftritt des Headliners kommt die Zugabe.

The difference is mainly focus:

• Die Zugabe ... puts the spotlight on the encore
• Nach dem Auftritt des Headliners ... puts the spotlight on when it happens

In both sentences, kommt stays in second position, which is one of the most important word-order rules in German main clauses.

Not only, but that is one very common meaning.

Zugabe can mean:

• an encore in a concert or performance context
• an extra amount or something added on in other contexts

The basic idea is something given in addition.

But in a sentence about a Headliner and an Auftritt, the meaning encore is the natural one.