Arinninn er í stofunni.

It is made of:

• arinn = fireplace
• -inn = the suffixed definite article, meaning the

So arinninn means the fireplace.

It looks a bit unusual because the base word arinn already ends in -nn, and then the definite ending is added after that.

In Icelandic, the definite article is usually attached to the end of the noun instead of being a separate word.

So:

• arinn = a fireplace / fireplace
• arinninn = the fireplace

And similarly:

• stofa = a living room / living room
• stofan / stofunni = the living room in different cases

This is one of the big differences from English.

Because í governs a case, and here it is expressing location: being in something.

When í means in in a static location, it normally takes the dative case.
The noun stofa changes form in the dative, and with the definite article attached, you get stofunni.

So:

• stofa = base form
• í stofunni = in the living room

This is a very important Icelandic pattern:

• í + dative = location, in
• í + accusative = movement, into

So:

• Arinninn er í stofunni. = The fireplace is in the living room.
• Hann fer í stofuna. = He goes into the living room.

In your sentence, the fireplace is not moving, so dative is used: í stofunni.

er is the present tense of að vera (to be).

Here it means is.

So the pattern is:

• arinninn = subject
• er = is
• í stofunni = location phrase

In this sentence, yes. It follows a very familiar pattern:

• Arinninn = subject
• er = verb
• í stofunni = prepositional phrase

So it works like The fireplace is in the living room.

However, Icelandic is a verb-second language in main clauses, so if you move another element to the front, the verb still usually stays in second position:

• Í stofunni er arinninn.

That is also correct, with a different emphasis.

• arinn is masculine
• stofa is feminine

Gender matters in Icelandic because it affects:

• the form of the definite article
• adjective endings
• some pronouns
• case forms

That is part of why you see different endings in arinninn and stofunni.

That ending reflects two things at once:

1. the noun is in the dative singular
2. it is definite: the living room

The noun stofa changes in the dative, and then the definite ending is added.
So stofunni is not random; it is a regular grammatical form.

For a learner, it is often easiest to think of it as:

• stofa = living room
• stofunni = in the living room / to the living room, depending on the construction

Then later you can learn the full declension pattern.

Yes, but it means something different.

• Arinninn er í stofunni. = The fireplace is in the living room.
• Arinn er í stofunni. = A fireplace is in the living room or just Fireplace is in the living room, depending on context

Without the definite ending, the noun is not specifically the fireplace.

í is pronounced roughly like ee in see.

The accent mark in Icelandic is not just decorative. It usually marks a different vowel sound, not simply stress.

So í is its own vowel letter in Icelandic and should be learned as such.

A rough English-friendly approximation is:

AH-rin-ninn er ee STOH-vun-ni

A few helpful points:

• Stress usually falls on the first syllable in Icelandic words.
• í sounds like ee.
• stofunni has a short u sound that does not match English perfectly, so any approximation is only rough.

If you want a more Icelandic-like rhythm, think:

AH-rin-ninn er ee STOH-vu-nni