Póstkassinn er við hurðina, en glugginn á svölunum er opinn.

Those endings are the Icelandic definite article, which is usually added to the end of the noun instead of being a separate word like English the.

So here:

• póstkassi = mailbox

• póstkassinn = the mailbox

• hurð = door

• hurðina = the door

• svalir = balcony / balconies
• svölunum = on the balcony / balconies, in dative plural definite form

The exact ending changes depending on gender, number, and case.

Because við normally takes the accusative case in modern Icelandic.

So:

• hurð = door
• hurðina = the door, accusative singular definite

In this sentence, við hurðina means by the door or next to the door.

The preposition á changes case depending on meaning:

• á + accusative often shows motion toward something
• á + dative often shows location in/on something

Here the meaning is static location: the window is located on the balcony, not moving onto it. So Icelandic uses dative:

• á svölunum = on the balcony

Because svalir is one of those Icelandic nouns that is normally plural in form, even when English uses a singular word.

So:

• svalir can mean a balcony
• á svölunum usually means on the balcony

This is very common and natural in Icelandic. You just have to learn svalir as a plural-form noun.

That is due to a vowel change called umlaut in Icelandic declension.

The base form is:

• svalir

But in some inflected forms, the a changes to ö:

• svölum
• svölunum

So á svölunum is the correct declined form.

Because the adjective must agree with the noun it describes.

Here opinn describes glugginn:

• gluggi = window
• glugginn = the window

Gluggi is masculine singular, and here it is in the nominative, so the adjective also appears in masculine singular nominative:

• opinn = open

Compare:

• hurðin er opin = the door is open
• opið would be neuter

Yes, við can have several meanings depending on context. In this sentence it means:

• by
• next to
• at

So við hurðina means by the door.

It does not mean with here.

It is a prepositional phrase that describes which window we are talking about.

So the structure is:

• glugginn = the window
• á svölunum = on the balcony

Together:

• glugginn á svölunum = the window on the balcony

It functions like a descriptive phrase attached to the noun.

Because Icelandic usually puts the onto the end of the noun instead of using a separate article.

So English:

• the mailbox
• the door
• the window

becomes Icelandic:

• póstkassinn
• hurðina
• glugginn

Icelandic does have separate article forms in some contexts, but the attached article is by far the most common pattern.

Because the sentence has two separate clauses joined by en:

• Póstkassinn er við hurðina
• en glugginn á svölunum er opinn

Each clause needs its own finite verb, and here that verb is er = is.

En means but here. It connects the two parts of the sentence and shows a contrast:

• the mailbox is by the door,
• but the window on the balcony is open.

It is a very common coordinating conjunction in Icelandic.

The dictionary forms are:

• póstkassi = mailbox
• hurð = door
• gluggi = window
• svalir = balcony

These are the forms you would usually look up in a dictionary. The sentence uses inflected versions of them:

• póstkassinn
• hurðina
• glugginn
• svölunum