Í anddyrinu er nýr dyrasími sem virkar loksins vel.

It is the dative singular definite form of anddyri.

That happens because í can take:

• dative for location: in
• accusative for motion into something: into

Here the meaning is location, so Icelandic uses the dative:

• í anddyrinu = in the hallway / in the entrance hall

If it meant motion, you would expect:

• í anddyrið = into the hallway

In Icelandic, the definite article is usually a suffix, not a separate word.

So:

• anddyri = an entrance hall / a vestibule
• anddyrið = the entrance hall
• anddyrinu = in the entrance hall or to the entrance hall, depending on context and case

So -nu here is part of the definite dative ending.

Because Icelandic often puts the setting or location first, especially when introducing something new.

The sentence structure is very natural for:

• first: where
• then: the verb
• then: what is there

So:

• Í anddyrinu er nýr dyrasími
  literally: In the entrance hall is a new intercom

This also follows Icelandic’s verb-second pattern: when a phrase other than the subject comes first, the finite verb still stays in the second position.

A more subject-first version is also grammatical:

• Nýr dyrasími er í anddyrinu

But the original sounds more natural if you are first telling someone where something is.

Because Icelandic normally does not use a separate indefinite article like English a/an.

So:

• nýr dyrasími = a new intercom

The noun phrase is understood as indefinite from context and form. Icelandic marks definiteness much more strongly than indefiniteness.

Because nýr agrees with dyrasími, which is:

• masculine
• singular
• nominative

So the adjective must also be:

• masculine singular nominative → nýr

This is the normal agreement pattern in Icelandic.

Very roughly:

• nýr = masculine nominative singular
• nýja / nýjan / nýtt / nýju = other genders/cases/forms

Here nýr dyrasími is the noun phrase being presented as what is in the hallway, so nominative is the expected form.

It is a compound noun:

• dyra-
  • sími

sími means telephone / phone, and dyrasími is basically a door phone, meaning an intercom or entry phone.

The first part, dyra-, is a compound form related to door/entrance. Icelandic makes compounds very freely, so this kind of long noun is extremely common.

sem introduces a relative clause.

So:

• nýr dyrasími sem virkar loksins vel
  = a new intercom that finally works well

The clause sem virkar loksins vel describes dyrasími.

A useful thing for learners: sem does not change form for gender or number here. It works as a general relative word like that/which/who in English.

virkar is the present-tense form of virka, meaning to work / to function.

So:

• virka = to function
• virkar = works / is working

This verb is very commonly used for machines, devices, systems, apps, and electronics. So for an intercom, virkar is exactly what you would expect.

Because it refers back to dyrasími, which is singular.

In the relative clause:

• sem virkar loksins vel

the subject is understood as the intercom. Since there is only one intercom, the verb is singular.

If it referred to a plural noun, the verb form would be plural.

loksins means finally or at last.

In this sentence it modifies the idea of the intercom’s functioning:

• virkar loksins vel = finally works well

Its placement is natural because it comes between the verb and vel, giving a smooth rhythm and the meaning it works well now, after a delay or frustration.

Because vel is an adverb, and it modifies the verb virkar.

You need an adverb when you describe how something works:

• virkar vel = works well

By contrast, góður/gott are adjectives and describe nouns or follow to be:

• Síminn er góður = The phone is good
• Síminn virkar vel = The phone works well

So in this sentence, vel is the correct choice.