Døren fører til bowlinghallen.

Because døren is the definite singular form: the door.

• en dør = a door
• døren = the door

In Danish, the definite article is often added to the end of the noun as a suffix, instead of being a separate word like the in English.

So:

• Døren fører til bowlinghallen. = The door leads to the bowling alley.

For the same reason: bowlinghallen is the definite singular form, meaning the bowling alley / the bowling hall.

• en bowlinghal = a bowling alley
• bowlinghallen = the bowling alley

In Danish compounds, the definite ending usually goes on the last part of the compound:

• bowling + hal = bowlinghal
• bowlinghal + en = bowlinghallen

So the whole phrase means to the bowling alley, not just to a bowling alley.

Because Danish normally writes compound nouns as one word.

So English-style combinations like:

• bowling hall
• school door
• city center

often become single words in Danish:

• bowlinghal
• skoledør
• bycenter

That means bowlinghallen is the normal Danish spelling, not bowling hallen.

Fører is the present tense of at føre.

• at føre = to lead, to conduct, to carry, depending on context
• fører = leads

In this sentence, fører til means leads to.

So:

• Døren fører til bowlinghallen.
• The door leads to the bowling alley.

This is a very natural use in Danish for talking about where a door, road, hallway, or staircase goes.

Because the expression is føre til, which means lead to.

Examples:

• Vejen fører til byen. = The road leads to the town.
• Trappen fører til første sal. = The stairs lead to the first floor.

So in this sentence:

• fører til bowlinghallen = leads to the bowling alley

A learner might wonder about i, but i would mean in. Here the idea is destination or connection, so til is the natural choice.

It can be both.

Physical:

• Døren fører til bowlinghallen.
• The door leads to the bowling alley.

Abstract:

• Det fører til problemer.
• That leads to problems.

So føre til works a lot like English lead to.

The tricky sound for English speakers is ø.

A rough guide:

• døren sounds approximately like DUHR-en, but with a rounded vowel that English does not really have
• fører sounds approximately like FUHR-er, again with ø

Important points:

• ø is not like English o
• You round your lips more than for English uh
• The r in Danish often affects the vowel and is not always pronounced strongly like in English

A rough full-sentence pronunciation guide could be:

DUR-en FUR-er til BOWL-ing-hal-en

But that is only approximate. The real Danish vowels are different from English ones.

The sentence has normal Danish main-clause word order:

• Døren = subject
• fører = verb
• til bowlinghallen = prepositional phrase

So the pattern is:

Subject + Verb + Prepositional phrase

That is very similar to English here:

• The door leads to the bowling alley.

Danish main clauses are generally verb-second language, and this sentence follows that rule naturally because the subject comes first and the verb comes second.

The dictionary forms are:

• dør / en dør = door
• bowlinghal / en bowlinghal = bowling alley
• at føre = to lead

The forms in the sentence are inflected versions:

• døren = definite singular of dør
• fører = present tense of at føre
• bowlinghallen = definite singular of bowlinghal

Yes, that would also be understandable and natural in many contexts.

• føre til = lead to
• lede til = also lead to

In a sentence about a door, road, corridor, or staircase, both can work.
However, fører til is perfectly good and idiomatic here.

So:

• Døren fører til bowlinghallen.
• Døren leder til bowlinghallen.

Both can mean The door leads to the bowling alley.

Yes, both nouns here are common gender nouns, and their definite singular ending is -en.

• en dør → døren
• en bowlinghal → bowlinghallen

Danish has two grammatical genders:

• common gender: usually takes en
• neuter: usually takes et

If a noun were neuter, the definite singular ending would usually be -et instead.

So seeing -en here tells you these nouns are common gender nouns.