Auf der Bordkarte stehen die Flugnummer und der Flugsteig.

Because auf can take either the dative or the accusative, depending on meaning.

• dative = location, when something is already somewhere
• accusative = direction/movement toward somewhere

Here, the sentence is about information being on the boarding pass, so this is a location idea, not movement. That is why German uses the dative:

• die Bordkarte → feminine noun
• dative feminine article = der
• so: auf der Bordkarte

If it were about putting something onto the boarding pass, then accusative would be used:

• Ich schreibe etwas auf die Bordkarte.

In German, stehen is very often used for text or information that is written or printed somewhere.

So:

• Auf der Bordkarte stehen ... = On the boarding pass, there are / it says ...
• literally, it is like saying the flight number and gate stand on the boarding pass

This is natural German. English usually says is/are written or simply the boarding pass shows. German often prefers stehen for this kind of context.

You will see the same pattern in sentences like:

• Auf dem Schild steht ... = The sign says ...
• In der E-Mail steht ... = The email says ...

Because the subject is actually two things together:

• die Flugnummer
• der Flugsteig

They are joined by und, so together they form a plural subject. That is why the verb is plural:

• singular: Die Flugnummer steht auf der Bordkarte.
• plural: Die Flugnummer und der Flugsteig stehen auf der Bordkarte.

Even though each noun is singular by itself, the combination of both makes the verb plural.

This is because German is a verb-second language in main clauses.

The first position in the sentence is occupied by:

• Auf der Bordkarte

Once that first element is placed at the front, the finite verb must come next:

• Auf der Bordkarte stehen ...

Only after the verb do we get the subject:

• die Flugnummer und der Flugsteig

So the basic idea is:

• first position: Auf der Bordkarte
• second position: stehen
• then: die Flugnummer und der Flugsteig

A more neutral order would be:

• Die Flugnummer und der Flugsteig stehen auf der Bordkarte.

Both are correct. The given version emphasizes where the information appears.

They are in the nominative case, because they are the subject of the sentence.

You can tell because they are the things that stand on the boarding pass:

• die Flugnummer = nominative singular feminine
• der Flugsteig = nominative singular masculine

Together they form the plural subject of stehen.

Because German nouns have grammatical gender, and these two nouns happen to have different genders:

• die Flugnummer = feminine
• der Flugsteig = masculine

There is no special rule in this sentence causing that difference; it is simply part of the nouns themselves and must be learned with the article.

It helps to memorize them as full units:

• die Flugnummer
• der Flugsteig
• die Bordkarte

Yes, here der Flugsteig means gate at the airport.

In everyday German, especially in airports, you will also often hear the English loanword:

• das Gate

So both of these can refer to the departure gate:

• der Flugsteig
• das Gate

Depending on region and context, Gate may sound more common in modern travel situations, but Flugsteig is a perfectly correct German word.

Yes, die Bordkarte is a correct word for boarding pass.

You may also come across:

• die Boardingkarte
• der Boardingpass

In practice, airlines and airports may use different terms, and English-influenced forms are also common. But Bordkarte is standard and fully understandable German.

Not naturally. There are two issues:

1. sein is less idiomatic here than stehen
   German prefers stehen for written information.

2. With two nouns joined by und, the verb would have to be plural anyway:

   • ... sind die Flugnummer und der Flugsteig

So the more natural German sentence is:

• Auf der Bordkarte stehen die Flugnummer und der Flugsteig.

That is the standard way to express this idea.

The core sentence is:

• Die Flugnummer und der Flugsteig stehen auf der Bordkarte.

Pattern:

• Subject: Die Flugnummer und der Flugsteig
• Verb: stehen
• Prepositional phrase: auf der Bordkarte

The original sentence simply moves the prepositional phrase to the front:

• Auf der Bordkarte stehen die Flugnummer und der Flugsteig.

So this is a good example of how German changes word order for emphasis while keeping the verb in second position.