Fanginn er í fangelsinu.

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

So here:

• fangi = prisoner
• fanginn = the prisoner

and

• fangelsi = prison
• fangelsinu = in the prison

The endings that express the change depending on gender, number, and case.

Because fanginn is the definite form: the prisoner.

More specifically:

• fangi = a prisoner
• fanginn = the prisoner

It is also in the nominative singular, because it is the subject of the sentence.

So:

• Fanginn = the subject
• er = is
• í fangelsinu = in the prison

Because the preposition í takes the dative case when it means in in the sense of location.

Here the prisoner is located inside the prison, so Icelandic uses the dative:

• fangelsi = prison
• fangelsinu = in the prison

If you used fangelsið, that would be the nominative/accusative definite form, not the dative form needed here.

So:

• í fangelsinu = in the prison

Not always. Í can take either dative or accusative, depending on meaning.

A useful rule:

• dative = location, being somewhere
• accusative = motion into somewhere

In this sentence:

• Fanginn er í fangelsinu = The prisoner is in the prison
  → location
  → dative

Compare that with a motion idea:

• Þeir settu fangann í fangelsið = They put the prisoner into the prison
  → movement into
  → accusative

Yes. Er is the 3rd person singular present tense of vera, which means to be.

So:

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

In Fanginn er í fangelsinu, er means is.

Yes, it matters a lot in Icelandic because gender affects endings.

Here:

• fangi is masculine
• fangelsi is neuter

That helps explain the different definite forms:

• masculine nominative singular definite: fanginn
• neuter dative singular definite: fangelsinu

So the endings are different partly because the nouns belong to different genders.

Because they are related words.

• fangi = prisoner
• fangelsi = prison

They share the same root idea, roughly connected with captivity or being held. This is similar to how English has related words like prisoner and prison.

That can make the sentence easier to remember.

Because í usually means in, inside, while á often means on or sometimes at, depending on the place.

A prison is thought of as an enclosed place, so Icelandic uses:

• í fangelsinu = in the prison

Using á here would sound wrong in normal Icelandic.

Not quite in the most natural sense.

Fanginn er í fangelsinu most literally means:

• The prisoner is in the prison
• or The prisoner is in the jail

It sounds like a specific prison is being referred to.

If you want the more general English idea in prison, Icelandic often says:

• Fanginn er í fangelsi

So the version with -nu is more specific and definite.

Yes, in this sentence it is very similar to English:

• Fanginn = subject
• er = verb
• í fangelsinu = prepositional phrase

So the structure is:

• Subject + verb + place

That said, Icelandic can move elements around more freely than English for emphasis. For example:

• Í fangelsinu er fanginn

is possible, but the neutral basic order is:

• Fanginn er í fangelsinu

A rough learner-friendly approximation is:

• FAHN-ginn er ee FAHN-gel-si-nu

Helpful pronunciation notes:

• Stress usually falls on the first syllable of Icelandic words.
• í sounds like ee in see.
• The final syllables are lighter and less stressed.

A rough stress pattern would be:

• FANginn er í FANgelsinu

Here is the full breakdown:

• Fanginn = the prisoner

  • noun
  • masculine
  • singular
  • nominative
  • definite

• er = is

  • verb
  • present tense of vera

• í = in

• fangelsinu = the prison / the jail

  • noun
  • neuter
  • singular
  • dative
  • definite

So the sentence is a very typical Icelandic pattern:

• subject + verb + prepositional phrase