Den venstre døren er stengt.

This is because of double definiteness, which is a normal feature of Norwegian.

• døren = the door
• When you add an adjective before a definite noun, Norwegian usually also adds den / det / de
• So den venstre døren literally looks like the left the-door

This is the standard pattern in Bokmål:

• døren = the door
• den store døren = the big door
• den venstre døren = the left door

English only uses one definite marker, but Norwegian often uses two in this kind of phrase.

Because dør is a common-gender noun in Norwegian.

Its basic form is:

• en dør = a door

Common-gender nouns use den in phrases like this:

• den venstre døren

If it were a neuter noun, you would use det instead:

• et hus = a house
• det store huset = the big house

So the choice of den comes from the gender of dør.

In definite noun phrases, adjectives often appear in an -e form:

• den store døren
• den gamle bilen

With venstre, the form is already venstre, so it stays the same:

• den venstre døren

Also, venstre is commonly used as a side/direction adjective, and it does not take any extra ending here.

It comes from the verb å stenge = to close / to shut, but here it is being used like an adjective.

So:

• er = is
• stengt = closed / shut

Together, er stengt means is closed.

This is very common in Norwegian. A past participle is often used after er to describe a state:

• Døren er stengt = The door is closed
• Butikken er stengt = The shop is closed

So in this sentence, stengt describes the condition of the door.

Not necessarily.

stengt means closed or shut. A door can be stengt without being locked.

If you specifically want to say locked, Norwegian usually uses:

• låst = locked

So:

• Døren er stengt = The door is closed
• Døren er låst = The door is locked

Sometimes a closed door may also be locked in real life, but the word stengt itself does not mean that.

Er is the present tense of å være = to be.

The sentence has a very simple structure:

• Den venstre døren = the subject
• er = the verb
• stengt = the description

So the whole sentence follows the pattern:

subject + verb + description

That is the same basic idea as in English:

• The left door is closed

Yes. In Bokmål, both are possible.

You may see:

• døren
• døra

Both mean the door.

In general:

• døren can sound more neutral or formal
• døra can sound more colloquial or more clearly feminine

So these are both possible:

• Den venstre døren er stengt
• Den venstre døra er stengt

Yes, absolutely.

That means roughly:

• The door on the left is closed

This version is often very natural when you are identifying something by location.

There is a small difference in feel:

• den venstre døren = the left door
• døren til venstre = the door on the left

Both are correct. Depending on context, some speakers may find døren til venstre a little more natural in everyday speech.

Because this is a normal Norwegian main clause.

The order is:

• Den venstre døren = subject
• er = finite verb
• stengt = complement/predicate

Norwegian main clauses usually follow the verb-second rule, often called V2. That means the finite verb usually comes in the second position.

Here, the subject comes first, so er comes second:

• Den venstre døren er stengt

That is the standard word order for a simple statement like this.