Í löngu setningunni finn ég frumlagið fyrst, en andlagið seinna.

Because í can take different cases depending on meaning.

• When í means movement into something, it usually takes the accusative.
• When it means being in something, it usually takes the dative.

Here the idea is location, not movement, so setning is in the dative singular: setningunni.

The adjective is löngu because:

• setning is feminine singular
• the noun is definite: the sentence
• adjectives before a definite noun usually take the weak form

So:

• indefinite: í langri setningu
• definite: í löngu setningunni

That ending includes the definite article and the dative singular ending.

The base noun is setning = sentence.
Its definite form in the dative singular is setningunni = the sentence after a preposition requiring dative.

So the ending reflects two things at once:

• case: dative
• definiteness: the

This is very normal in Icelandic, where the definite article is usually attached to the end of the noun.

This is a classic example of Icelandic V2 word order.

In main clauses, the finite verb usually comes in the second position. The first position does not have to be the subject. It can be an adverb, a prepositional phrase, an object, and so on.

Here the first element is the whole phrase:

• Í löngu setningunni

Since that takes first position, the verb must come next:

• Í löngu setningunni finn ég ...

If you started with the subject instead, you would get:

• Ég finn frumlagið fyrst í löngu setningunni ...

So finn ég is not unusual or poetic here; it is normal Icelandic sentence structure.

These are grammar terms.

• frumlag = subject
• andlag = object

With the definite article attached, they become:

• frumlagið = the subject
• andlagið = the object

So the sentence is talking about identifying parts of a sentence: first the subject, then the object.

Because both nouns are neuter singular definite nouns.

The base forms are:

• frumlag
• andlag

Add the suffixed definite article, and you get:

• frumlagið
• andlagið

Also, in this sentence they are the objects of the verb finna, which normally takes the accusative. For many neuter nouns, the nominative and accusative singular look the same, so -ið fits naturally here.

They are functioning as the direct objects of finna, so they are in the accusative.

That is easiest to see with the full underlying structure:

• Ég finn frumlagið fyrst, en [ég finn] andlagið seinna.

Both frumlagið and andlagið are things being found, so both belong with finna and are therefore accusative.

However, because these are neuter singular nouns, the accusative form looks the same as the nominative form.

Because Icelandic often leaves out repeated words when they are easy to understand from context.

The full version would be something like:

• Í löngu setningunni finn ég frumlagið fyrst, en ég finn andlagið seinna.

But that sounds more repetitive. Icelandic, like English, often omits the repeated verb phrase in coordinated clauses:

• I find the subject first, but the object later.

So en andlagið seinna is a natural shortened form.

Because they are adverbs, not adjectives.

They describe when or in what order the finding happens:

• fyrst = first
• seinna = later

They modify the action finn rather than describing a noun.

Compare:

• fyrsta orðið = the first word → adjective describing a noun
• ég finn það fyrst = I find it first → adverb describing the action

Seinna here means later, not necessarily the second one in a strict numbered sequence.

Here it means but.

The sentence is making a contrast:

• first the subject
• later the object

So en is connecting two contrasting parts, which English usually expresses with but.

In many contexts, en is the normal Icelandic word for but.

Because the speaker is referring to specific things already understood in context.

• setningunni = a particular sentence being discussed
• frumlagið = the subject of that sentence
• andlagið = the object of that sentence

This is very natural in explanations about grammar. Once a specific sentence is under discussion, Icelandic often uses definite forms for the parts being identified.