Forsetningin í þessari setningu er ekki rétt.

It is the definite article attached to the noun.

• forsetning = a preposition
• forsetningin = the preposition

This is very common in Icelandic. Instead of a separate word like English the, Icelandic usually adds the article to the end of the noun.

In this sentence, forsetningin is nominative singular definite.

Because the preposition í here is followed by the dative case.

That affects both words:

• þessi becomes þessari in the dative feminine singular
• setning becomes setningu in the dative singular

So:

• þessi setning = this sentence
• í þessari setningu = in this sentence

English does not change this sentence after in, but Icelandic does.

Í can take either dative or accusative, depending on meaning:

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

In your sentence, it means in this sentence as a location, so Icelandic uses the dative:

• í þessari setningu

Compare:

• Hann er í húsinu. = He is in the house.
• Hann fer í húsið. = He goes into the house.

So the case after í is controlled by whether the meaning is static or directional.

Yes. Þessari is one form of the demonstrative þessi, which means this.

The form changes for gender, number, and case.

Here it modifies setningu, and setning is:

• feminine
• singular
• dative

So þessi must also be feminine singular dative, which is þessari.

Because when you use a demonstrative like þessi (this), the noun normally does not also take the suffixed definite article.

So Icelandic usually says:

• þessi setning = this sentence

not:

• *þessi setningin

That is why the phrase is í þessari setningu, not í þessari setningunni.

A good simple rule is: if þessi is there, you normally do not add the noun’s definite ending as well.

Because adjectives in Icelandic usually agree with the noun they describe.

Here rétt is a predicative adjective after er:

• Forsetningin ... er ekki rétt.

The subject forsetningin is feminine singular, and the feminine singular form of réttur is rétt.

So:

• masculine: réttur
• feminine: rétt
• neuter: rétt

That means rétt is the correct form here, even though it looks the same as the neuter form.

Because in a normal Icelandic main clause, the finite verb usually comes early, and ekki usually comes after it.

So:

• er ekki rétt = is not correct

This is the normal neutral order.

A useful beginner pattern is:

• Subject + verb + ekki + rest

So this sentence follows a very common Icelandic structure.

Yes, both are feminine.

That matters because feminine nouns affect:

• the form of this: þessi / þessari
• the form of adjectives: rétt
• noun endings in different cases: setning → setningu

So part of understanding this sentence is recognizing that both main nouns are feminine.

Yes, that is possible, but it is slightly different in tone.

• ekki rétt = not correct
• röng = wrong / incorrect

Since forsetningin is feminine singular, the adjective would be röng, not rangt.

So:

• Forsetningin í þessari setningu er ekki rétt.
• Forsetningin í þessari setningu er röng.

Both can work, but ekki rétt can sound a little softer or less direct than röng.

Yes. The whole noun phrase Forsetningin í þessari setningu functions as the subject.

You can think of it like this:

• Forsetningin = the head noun
• í þessari setningu = a prepositional phrase describing which preposition

So the sentence structure is:

• [Subject] Forsetningin í þessari setningu
• [Verb] er
• [Negation + complement] ekki rétt

That is why the sentence means that a particular preposition, namely the one found in this sentence, is not correct.