Metroens indgang er på venstre side.

Metroens comes from metroen + -s.

• metro = metro
• metroen = the metro
• metroens = the metro’s / of the metro

So Metroens indgang literally means the metro’s entrance, though in natural English that is often expressed as the entrance to the metro.

Because after a possessive or genitive form like metroens, Danish normally uses the noun in its indefinite form.

So:

• metroens indgang = the metro’s entrance

Not:

• metroens indgangen

This is the same pattern as:

• Peters bil = Peter’s car
• husets tag = the house’s roof / the roof of the house

Even though the whole phrase is definite in meaning, the noun itself stays indefinite after the possessor.

Yes, absolutely. That is also natural Danish.

• Metroens indgang = the metro’s entrance
• Indgangen til metroen = the entrance to the metro

Both are correct. In everyday Danish, the til version can often sound a bit more natural, especially with places:

• indgangen til metroen
• døren til huset
• vejen til stationen

So the original sentence is correct, but there is a very common alternative.

Because på venstre side is the normal expression for on the left side.

Here på works the same way English on does in this kind of phrase:

• på venstre side = on the left side
• på højre side = on the right side

You would not normally say i venstre side here.

Venstre means left, and in this kind of expression it stays as venstre.

So you get:

• venstre side = left side
• højre side = right side

Words like venstre and højre do not usually change form the way many other Danish adjectives do. So you just learn them as fixed forms in expressions like:

• til venstre
• på venstre side
• højre hånd
• venstre ben

Yes. That would also be correct.

• Metroens indgang er til venstre = The metro entrance is to the left / on the left
• Metroens indgang er på venstre side = The metro entrance is on the left side

Til venstre is shorter and very common in spoken Danish.
På venstre side sounds a little more explicit.

The sentence follows normal Danish main-clause word order:

• Metroens indgang = subject
• er = verb
• på venstre side = location phrase

So the structure is:

subject + verb + adverbial

Danish is a V2 language, which means the finite verb normally comes in the second position in a main clause. Since the subject comes first here, er comes second.

Here Danish uses the indefinite noun in a fixed location expression:

• på venstre side

This is similar to other common expressions where Danish does not use the definite form even though English may sound definite.

If you say på den venstre side, that becomes more specific or contrastive, like on the left-hand side or on that left side. The original sentence is more neutral and natural.

Literally, yes. But the most natural English translation is often the entrance to the metro.

That is important because Danish often uses a possessive/genitive structure where English prefers an of phrase or a to phrase.

So:

• Metroens indgang = literally the metro’s entrance
• natural English: the entrance to the metro

This is a very common difference between the two languages.