Í húsinu býr eldri íbúi á hæðinni fyrir ofan okkur sem gengur niður stigaganginn á hverjum morgni.

This is because Icelandic follows a V2 pattern in main clauses: the finite verb usually comes in the second position.

So if you start the sentence with Í húsinu (in the house/building), the verb býr has to come next:

• Í húsinu býr eldri íbúi...

If you started with the subject instead, that would also be correct:

• Eldri íbúi býr í húsinu...

Both are grammatical, but the original sentence puts focus first on where this person lives.

Because í can take either:

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

Here the meaning is static location, not movement:

• í húsinu = in the house/building

So the noun is in the dative singular definite form:

• hús = house/building
• húsinu = the house/building in the dative

Compare:

• Ég er í húsinu = I am in the house
• Ég fer í húsið = I go into the house

Býr is the present tense, 3rd person singular form of að búa.

In this sentence it means lives:

• býr = lives

It agrees with the subject eldri íbúi, which is singular:

• eldri íbúi býr = an older resident lives

This verb can also mean things like resides or sometimes dwells, depending on context.

Eldri is the comparative form related to gamall (old), and here it means older.

So:

• gamall = old
• eldri = older

In context, eldri íbúi can mean:

• an older resident
• sometimes more naturally, an elderly resident, depending on the situation

A useful thing to know is that comparative adjective forms like eldri often stay the same across many grammatical contexts, so you will see eldri very often without many visible ending changes.

Because the phrase is indefinite:

• eldri íbúi = an older resident
• eldri íbúinn = the older resident

The sentence is introducing this person as one resident of the building, not as a specifically identified resident already known to the listener.

This is just the normal Icelandic idiom for floors/storeys of a building.

Icelandic says:

• á hæð = on a floor/storey

So:

• á hæðinni = on the floor

Even though English often says on the floor too, learners sometimes expect í because a floor feels like something inside a building. But Icelandic uses á here.

Also, because this is a location, á takes the dative:

• hæðinni = the floor/storey (dative singular definite)

Because they are being used differently.

• eldri íbúi is indefinite: an older resident
• hæðinni is definite: the floor

The floor is made specific by the phrase that follows:

• á hæðinni fyrir ofan okkur = on the floor above us

So it is not just any floor; it is a particular floor, namely the one above us.

Fyrir ofan is a fixed expression meaning:

• above
• over

So:

• fyrir ofan okkur = above us

It modifies hæðinni:

• á hæðinni fyrir ofan okkur = on the floor above us

A helpful literal breakdown is:

• á hæðinni = on the floor
• fyrir ofan okkur = above us

Together: on the floor above us

Okkur is the form of við (we/us) used here after the expression fyrir ofan.

So:

• við = we
• okkur = us

In the phrase:

• fyrir ofan okkur = above us

For an English speaker, the main thing to remember is that Icelandic pronouns change form depending on grammar and prepositions, so you often need a different form than the dictionary form.

Sem introduces a relative clause. Here it means something like:

• who
• that

So:

• eldri íbúi ... sem gengur niður stigaganginn
  = an older resident ... who walks down the stairwell

A very useful point: sem does not change for gender, number, or person. Icelandic uses the same sem for:

• the man who...
• the woman who...
• the house that...

It describes the resident.

So the structure is:

• eldri íbúi ... sem gengur niður stigaganginn á hverjum morgni

That means:

• an older resident ... who walks down the stairwell every morning

It does not mean that the floor walks down the stairwell. Grammatically, the relative clause attaches to íbúi, and semantically only a person can ganga here.

Gengur is from að ganga, meaning to walk.

So:

• gengur niður stigaganginn = walks down the stairwell

The word niður means down, and stigaganginn is the definite form of stigagangur:

• stigagangur = stairwell / staircase area / stairway
• stigaganginn = the stairwell (accusative singular definite)

This whole phrase describes movement along a path downward.

Here the stairwell is being treated as the path of movement, so the noun appears in the accusative.

That is very common with verbs of motion and directional expressions:

• ganga niður stigaganginn = walk down the stairwell

By contrast, if you were talking about being located in the stairwell, you would use a different structure, for example:

• í stigaganginum = in the stairwell

So:

• stigaganginn = movement/path
• stigaganginum = location after a preposition like í

This is a common Icelandic time expression meaning:

• every morning

Literally it is closer to:

• on each morning

Breakdown:

• á = on
• hverjum = each/every (dative singular here)
• morgni = morning (dative singular)

Because á is used in this time expression, the noun phrase appears in the dative:

• á hverjum morgni = every morning

Yes. This is a productive pattern for repeated time expressions:

• á hverjum degi = every day
• á hverju kvöldi = every evening
• á hverju ári = every year

So á hverjum morgni fits a very common and useful structure.

Because Icelandic chooses prepositions based on the specific noun and the idiom involved, not just on a general idea like inside.

Here:

• í húsinu = in the building
• á hæðinni = on the floor/storey

That combination is perfectly normal in Icelandic. It is one of those places where the best approach is to learn the noun together with its usual preposition:

• í húsi
• á hæð