Om et øjeblik åbner dørene, og min søster spørger, om hendes plads er tæt på scenen eller længere tilbage.

Because Danish is a V2 language in main clauses. That means the finite verb usually comes in the second position.

So when the time expression Om et øjeblik is moved to the front, the verb åbner must come right after it, and the subject dørene comes after the verb.

• Dørene åbner om et øjeblik = neutral order
• Om et øjeblik åbner dørene = the time expression is emphasized

This kind of inversion is normal in Danish and does not mean it is a question.

Danish often uses the present tense for the near future or for something expected to happen soon, especially when there is a time expression like om et øjeblik.

So:

• Om et øjeblik åbner dørene = The doors will open in a moment
• min søster spørger can describe what happens next in a sequence

This is very natural in Danish, just as English can sometimes say I leave tomorrow.

Om et øjeblik means in a moment, in a second, or very soon.

Here, om is used in a time expression meaning something like in:

• om et minut = in a minute
• om en time = in an hour
• om lidt = in a little while

So om et øjeblik is a very common way to say that something will happen soon.

No. In Danish, verbs do not change form according to person or number in the present tense.

So the same form is used with:

• jeg åbner
• du åbner
• han åbner
• vi åbner
• dørene åbner

That is why åbner works perfectly with the plural subject dørene.

No. It is the same word in form, but here it has a different function.

In spørger, om..., om means whether or if and introduces an indirect yes/no question:

• Hun spørger, om hendes plads er tæt på scenen. = She asks whether/if her seat is close to the stage.

So in this sentence:

• first om = in a moment
• second om = whether/if

This is very common in Danish.

Because once you enter a subordinate clause introduced by om, Danish normally uses subject + verb order, not main-clause V2 order.

So:

• main clause: Om et øjeblik åbner dørene
• subordinate clause: om hendes plads er tæt på scenen

In other words:

• main clause often shows verb-second
• subordinate clause usually does not

This contrast is one of the key word-order patterns in Danish.

Because sin/sit/sine refers back to the subject of the same clause, and that is not what is happening here.

In the subordinate clause:

• om hendes plads er tæt på scenen

the grammatical subject is hendes plads, not min søster.

Also, sin normally cannot be used inside the subject phrase itself in this way. So hendes plads is the correct form here.

Compare:

• Min søster finder sin plads.
  Here sin works, because it refers back to min søster, the subject of the same clause.

But in your sentence, hendes is the natural and correct choice.

Danish often marks the by adding an ending to the noun.

Examples from the sentence:

• en scene = a stage

• scenen = the stage

• en dør = a door
• døre = doors
• dørene = the doors

But with possessives like min, din, hendes, vores, the noun does not take that definite ending:

• hendes plads = her seat
• not hendes pladsen

So:

• dørene = the doors
• scenen = the stage
• hendes plads = her seat

Tæt på means close to or near.

It is a very common expression, and på is the preposition that goes with tæt when you say what something is close to.

Examples:

• tæt på scenen = close to the stage
• tæt på mig = close to me
• tæt på centrum = close to the center

So you should learn tæt på as a unit, much like English close to.

It means further back or farther back.

• længere = comparative form, here meaning further/farther
• tilbage = back

So:

• tæt på scenen eller længere tilbage = close to the stage or farther back

You do not need an explicit than here, because the comparison is understood from the context. It is a very natural way to talk about seating or position in a room, hall, or theater.