Hvis der ikke er flere sæder, står jeg ved døren og kigger på skiltet over sporet for at se, om det er den rigtige linje.

This is because Danish follows the V2 rule in main clauses: the finite verb normally comes in the second position.

The sentence begins with a subordinate clause:

• Hvis der ikke er flere sæder = if there are no more seats

After that clause, the main clause starts. Since the if-clause takes the first position, the verb must come next:

• står jeg ved døren

So the pattern is:

• [subordinate clause], [verb] [subject] ...

That is why you get:

• Hvis der ikke er flere sæder, står jeg ved døren ...

and not:

• Hvis der ikke er flere sæder, jeg står ved døren ...

This is very common in Danish.

Here, der is a kind of dummy subject, similar to English there in sentences like:

• There are no more seats

So:

• der er flere sæder = there are more seats
• der ikke er flere sæder = there are not more seats / there are no more seats

This der does not mean there as a physical place. It just helps form an existence sentence.

Compare:

• Der er en stol herinde = There is a chair in here
• Jeg står der = I am standing there

In the second sentence, der really means a place. In your sentence, it does not.

Because flere is used with countable nouns meaning more or additional.

• et sæde = a seat
• flere sæder = more seats

You use mere mainly with:

• uncountable nouns
• adjectives
• adverbs

Examples:

• mere vand = more water
• mere interessant = more interesting
• arbejde mere = work more

Since sæder is a plural countable noun, flere is the correct choice.

In Danish, plural indefinite nouns often appear without any article, just as in English.

So:

• sæder = seats
• flere sæder = more seats

You do not need a word corresponding to some or any here.

Compare:

• Jeg har bøger = I have books
• Der er flere sæder = There are more seats

That is normal Danish grammar.

Yes. Danish often uses stå very naturally where English might also say be standing or even just be depending on context.

• står jeg ved døren = I stand / I am standing by the door

In Danish, verbs of position are used a lot:

• stå = stand
• sidde = sit
• ligge = lie
• hænge = hang

So Danish often describes how something is positioned, not just that it is somewhere.

Ved means by, near, or at.

So:

• ved døren = by the door / at the door

If you said i døren, that would sound more like in the doorway or physically in the door opening, which is a different image.

So in this sentence, ved døren is the natural choice for someone waiting or standing near the door.

Because kigge på is the normal expression for look at.

• kigge = look
• kigge på = look at

So:

• jeg kigger på skiltet = I look at the sign

This works like many verb + preposition combinations in English. The preposition is just part of the usual expression.

Compare:

• se på noget = look at something
• lytte til noget = listen to something
• tænke på noget = think about something

So på is required here.

Because Danish usually puts the definite article at the end of the noun.

• et skilt = a sign
• skiltet = the sign

This is very common in Danish:

• en dør = a door
• døren = the door
• et spor = a track
• sporet = the track

So skiltet literally contains the idea of the sign in one word.

Because Danish uses the definite form when referring to a specific track that is understood from the situation.

• et spor = a track
• sporet = the track

So:

• skiltet over sporet = the sign above the track

In context, this means a particular track the speaker is looking at.

It is also worth noticing that spor is a neuter noun, so its definite singular ending is -et:

• et spor
• sporet

For at means in order to or to, when expressing purpose.

So:

• kigger på skiltet for at se ... = look at the sign to see ... = look at the sign in order to see ...

This structure is extremely common in Danish:

• Jeg går ud for at købe mad = I go out to buy food
• Hun ringer for at spørge om noget = She calls to ask about something

So for at se tells you the purpose of looking at the sign.

Because se is in the infinitive, and Danish often uses at before the infinitive, similar to English to.

• at se = to see
• at gå = to go
• at være = to be

After for, you normally get for at + infinitive when expressing purpose:

• for at se
• for at finde
• for at vide

So for at se is a fixed and normal pattern.

Because here om means whether, not if in the conditional sense.

There are two different ideas:

• hvis = if, in a condition
• om = whether, in an indirect yes/no question

In your sentence:

• for at se, om det er den rigtige linje = to see whether it is the right line

That is not a condition. It is an embedded question.

Compare:

• Hvis det regner, bliver jeg hjemme = If it rains, I stay home
• Jeg ved ikke, om det regner = I do not know whether it is raining

That is the key difference.

Because after om, this is an embedded question, and Danish uses normal subordinate-clause word order:

• om det er den rigtige linje

The subject comes before the verb:

• det = subject
• er = verb

This is different from a direct question:

• Er det den rigtige linje? = Is it the right line?

So compare:

• Direct question: Er det den rigtige linje?
• Embedded question: Jeg vil se, om det er den rigtige linje

English works similarly:

• Is it the right line?
• I want to see whether it is the right line

Linje is a common-gender noun in Danish:

• en linje = a line

So the definite/pointing form is built with den:

• den rigtige linje = the right line

Here, den agrees with the gender of linje.

Compare:

• en stol → den store stol = the big chair
• et hus → det store hus = the big house

Because linje is en-words, you use den, not det.

Because when an adjective comes before a noun in a definite phrase, Danish usually uses the -e form.

So:

• en rigtig linje = a correct/right line
• den rigtige linje = the right/correct line

This -e form is very common in definite expressions:

• den store by = the big city
• det lille barn = the small child
• de gamle bøger = the old books

So den rigtige linje is the expected form.

Yes. The main finite verbs are all in the present tense:

• er = is / are
• står = stand / am standing
• kigger = look / am looking
• er = is

And se is an infinitive after at.

Danish present tense is often used in situations where English might use either:

• the simple present
• the present progressive

For example:

• jeg står ved døren can mean I stand by the door or more naturally I am standing by the door
• jeg kigger på skiltet can mean I look at the sign or I am looking at the sign

So the Danish present tense covers both ideas much more often than English does.