Jakken hænger ved siden af døren i gangen.

Because Danish often puts the definite article at the end of the noun instead of using a separate word like English the.

• en jakke = a jacket
• jakken = the jacket
• en dør = a door
• døren = the door
• en gang = a hallway / corridor
• gangen = the hallway

All three nouns here are common gender nouns, so their definite ending is -en.

Because Danish often prefers a position verb when describing where something is.

So instead of just saying the jacket is by the door, Danish says the jacket hangs by the door if the object is hanging.

This is very common:

• står = stands
• ligger = lies
• sidder = sits
• hænger = hangs

So Jakken hænger ... sounds natural because a jacket is typically hanging on a hook, hanger, or similar support.

It can mean both, depending on context.

In Danish, the simple present often covers both:

• it hangs
• it is hanging

So Jakken hænger ved siden af døren i gangen can naturally be understood as The jacket hangs / is hanging next to the door in the hallway.

The infinitive is at hænge = to hang.

In this sentence:

• hænger is the present tense

Danish verbs are simpler than English in one important way: they do not change for person.

• jeg hænger
• du hænger
• han/hun hænger

The form stays the same.

Ved siden af is a fixed expression meaning next to or beside.

Literally, it is something like:

• ved = by / at
• siden = the side
• af = of

So the whole phrase functions as one unit:

• ved siden af døren = next to the door

It is best learned as a chunk: ved siden af.

No, not in standard Danish.

The normal expression is:

• ved siden af døren

The af is part of the fixed phrase. If you leave it out, it will sound wrong to most speakers.

Because in Danish, when a noun is definite and there is no adjective before it, you usually use the suffix definite form:

• døren = the door

Den dør usually means that door in ordinary speech, or it can be part of a structure with an adjective:

• den røde dør = the red door

So here, døren is the natural choice.

They express two different kinds of location:

• ved siden af døren = next to the door
• i gangen = in the hallway

So:

• ved helps express proximity to the door
• i shows that the location is inside the hallway

English does the same kind of thing:

• next to the door
• in the hallway

Gang usually means hallway, corridor, or passage.

So i gangen means:

• in the hallway
• in the corridor

The best English translation depends on the building and situation, but hallway is usually the most natural choice.

In practice, it describes the whole situation: the jacket is hanging next to the door, and this is happening in the hallway.

A listener will usually picture:

• a door in the hallway
• the jacket hanging next to it

So even if there is a slight structural ambiguity, the meaning is normally clear from context.

Yes. It follows normal Danish main-clause word order:

• Jakken = subject
• hænger = verb
• ved siden af døren i gangen = place information

So the pattern is basically:

Subject + Verb + Adverbial

That is the most neutral way to say it.

Yes, but then the emphasis changes, and Danish follows the verb-second rule.

For example:

• I gangen hænger jakken ved siden af døren.

This puts more focus on in the hallway.

Notice that when I gangen comes first, the verb still stays in second position:

• I gangen
  • hænger
    • jakken

That is a very important Danish word-order pattern.

Because Danish usually expresses the by adding it to the end of the noun:

• jakken = the jacket
• døren = the door
• gangen = the hallway

English uses a separate word:

• the jacket

Danish usually uses a suffix instead:

• jakken

That is one of the biggest structural differences English speakers notice early on.