Skoðunarstofan er opin.

Because Icelandic usually puts the definite article onto the end of the noun instead of using a separate word like English the.

So:

• skoðunarstofa = an inspection/examination room or office
• skoðunarstofan = the inspection/examination room or office

Here -an is the feminine singular nominative definite ending. The base noun stofa is feminine, so its definite form is stofan.

Yes, it is one compound word, which is very common in Icelandic.

It breaks down like this:

• skoðun = inspection, examination
• skoðunar- = genitive form, used here as a linking first element
• stofa = room, office, clinic

So skoðunarstofa is literally something like inspection-room or examination-office.

The -ar comes from the genitive singular of skoðun. Icelandic often uses this kind of genitive form inside compounds.

Er is the present-tense form of the verb vera, which means to be.

So:

• vera = to be
• er = is

It is an irregular verb, and it is one of the most common verbs in Icelandic.

For comparison:

• ég er = I am
• þú ert = you are
• hann/hún/það er = he/she/it is

Because adjectives in Icelandic must agree with the noun in gender, number, and usually case.

The noun skoðunarstofan is:

• feminine
• singular
• nominative

So the adjective must also be feminine singular nominative:

• opinn = masculine singular
• opin = feminine singular
• opið = neuter singular

That is why the sentence uses opin.

This is a very common question.

After vera and similar linking verbs, Icelandic normally uses the strong/predicate form of the adjective, not the weak attributive form that you often see before a definite noun.

So:

• Skoðunarstofan er opin. = The inspection office is open.
• opna skoðunarstofan = the open inspection office

In other words:

• opin is the normal predicate form after er
• opna would be used when the adjective comes directly before the definite noun

English does not make this distinction, but Icelandic does.

The subject skoðunarstofan is in the nominative, and the adjective opin is also nominative because it agrees with the subject after vera.

So the structure is:

• skoðunarstofan = nominative subject
• er = is
• opin = nominative predicate adjective

This is the normal pattern with vera.

Yes, but the meaning changes.

• Skoðunarstofan er opin. = The inspection/examination office is open.
• Skoðunarstofa er opin. = An inspection/examination office is open, or more loosely inspection office is open

Icelandic has no indefinite article matching English a/an, so the bare noun skoðunarstofa can be indefinite.

In most normal situations, if you mean one specific known place, the definite form skoðunarstofan is the natural choice.

A rough English-friendly approximation is:

SKO-thu-nar-stoh-van

A few useful pronunciation points:

• ð is like the th in this
• ó is a long vowel
• the f in stofan is pronounced like v here, because it is between vowels

So stofan sounds closer to stovan than to stofan with an English f.

Only because it is the first word of the sentence.

In Icelandic, ordinary nouns are not capitalized the way they are in German. So if this word appeared in the middle of a sentence, it would normally be written skoðunarstofan, not Skoðunarstofan.