Auf der ersten Folie steht nur eine Frage, die wir im Seminarraum gemeinsam beantworten.

In German, stehen is very commonly used for written content that appears somewhere.

So:

• Auf der ersten Folie steht nur eine Frage. = On the first slide, there is only one question / only one question appears on the first slide.

German often uses:

• stehen for text written on a page, sign, slide, poster, etc.
• liegen for things physically lying somewhere
• sein in more general statements

So steht here sounds very natural because the question is written on the slide.

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

• dative = location, where something is
• accusative = direction, where something is going

Here the sentence describes a location:

• The question is on the first slide.

So German uses dative:

• auf der ersten Folie

If it were about movement onto the slide, you would use accusative:

• Ich schreibe die Frage auf die erste Folie. = I write the question onto the first slide.

So in your sentence, der is correct because this is a static location.

This is a combination of:

• the preposition auf
• the feminine noun die Folie
• the dative case
• the adjective erste

Since Folie is feminine, its article changes like this:

• nominative: die Folie
• accusative: die Folie
• dative: der Folie

That gives you auf der Folie.

Then the adjective erste also has to match the case, gender, and article:

• nominative feminine: die erste Folie
• dative feminine: der ersten Folie

So:

• auf der ersten Folie

is simply the correct dative feminine form.

In a normal German main clause, the finite verb goes in second position. This is the basic V2 rule.

Here, the first position is taken by the whole phrase:

• Auf der ersten Folie

Then the verb must come next:

• steht

So the structure is:

• Auf der ersten Folie | steht | nur eine Frage

Even though English often starts with the subject, German does not have to. The first position can be:

• a time phrase
• a place phrase
• an object
• the subject

As long as the finite verb stays in second position.

If you started with the subject instead, you could also say:

• Nur eine Frage steht auf der ersten Folie...

That is grammatically possible, though the original version sounds more natural in many contexts.

Here die is a relative pronoun. It refers back to eine Frage.

So:

• eine Frage, die wir ... beantworten = a question that we answer ...

The important point is that die is not the article the here. It means that / which.

It is feminine singular because it refers to die Frage.

Because the relative pronoun must match the noun it refers to in gender and number, but its case depends on its role inside the relative clause.

It refers to:

• eine Frage → feminine singular

Inside the relative clause, that question is the direct object of beantworten:

• wir beantworten die Frage

A direct object takes the accusative.

For a feminine singular noun, the relative pronoun is:

• nominative: die
• accusative: die
• dative: der
• genitive: deren

So the correct form here is die.

Because German relative clauses are separated by commas.

The part

• die wir im Seminarraum gemeinsam beantworten

is a relative clause describing eine Frage, so it must be set off with a comma.

This is standard German punctuation:

• Das ist der Mann, der dort sitzt.
• Ich lese ein Buch, das sehr spannend ist.

So the comma before die is required.

Im is a contraction of:

• in dem → im

So:

• im Seminarraum = in the seminar room

Also, in can take either dative or accusative:

• dative for location
• accusative for direction

Here it means a location, not movement:

• we answer it in the seminar room

So German uses dative:

• in dem Seminarraum
• contracted: im Seminarraum

Beantworten is a verb that takes a direct object in the accusative.

So you say:

• eine Frage beantworten
• die Frage beantworten

There is no extra preposition needed.

This is useful to remember because the related noun phrase uses a preposition:

• eine Antwort auf eine Frage = an answer to a question

But the verb is different:

• eine Frage beantworten = to answer a question

So in your sentence:

• die wir ... beantworten

the object is simply the relative pronoun die.

Nur means only.

In this sentence:

• Auf der ersten Folie steht nur eine Frage

it limits eine Frage:

• only one question

Its position is important. Placing nur before eine Frage makes it clear that the restriction applies to the noun phrase.

Compare:

• nur eine Frage = only one question
• wir beantworten die Frage nur im Seminarraum = only in the seminar room
• wir beantworten die Frage nur gemeinsam = only together

So nur usually stands close to the part it modifies.

Gemeinsam means together, jointly, or as a group.

In this sentence it describes how the question is answered:

• die wir im Seminarraum gemeinsam beantworten = that we answer together in the seminar room

Its placement is natural because German often puts adverbs like this in the middle field of the clause, often after place expressions or near the end.

You could move it for emphasis, but the original order is very normal:

• ..., die wir gemeinsam im Seminarraum beantworten.
• ..., die wir im Seminarraum gemeinsam beantworten.

Both are possible, but the second one sounds especially smooth here.

Because in a subordinate clause, such as a relative clause, the finite verb goes to the end.

So the clause is structured like this:

• die = relative pronoun
• wir = subject
• im Seminarraum = place
• gemeinsam = adverb
• beantworten = finite verb at the end

That gives:

• die wir im Seminarraum gemeinsam beantworten

This is one of the biggest differences from main clauses in German:

• Main clause: Wir beantworten die Frage.
• Relative clause: ..., die wir beantworten.

So seeing the verb at the end is completely normal here.

Yes. German word order is flexible, especially in the main clause, as long as the finite verb stays in second position.

For example, these are possible:

• Auf der ersten Folie steht nur eine Frage, die wir im Seminarraum gemeinsam beantworten.
• Nur eine Frage steht auf der ersten Folie, die wir im Seminarraum gemeinsam beantworten.

The first version is more natural because it starts with the location and sets the scene.

Inside the relative clause, there is also some flexibility:

• ..., die wir im Seminarraum gemeinsam beantworten.
• ..., die wir gemeinsam im Seminarraum beantworten.

The original order is clear and idiomatic, but German allows some movement for rhythm or emphasis.