Bíllinn er hraður.

Because Icelandic usually adds the definite article to the end of the noun instead of using a separate word like the.

• bíll = car
• bíllinn = the car

So Bíllinn er hraður literally breaks down as:

• bíll-inn = car-the
• er = is
• hraður = fast

This attached -inn is very common in Icelandic.

Yes, but it means something different.

• Bíll er hraður = A car is fast or Cars are fast in a very general sense, depending on context
• Bíllinn er hraður = The car is fast

So the -inn ending is important because it makes the noun definite.

Because Icelandic adjectives must agree with the noun they describe in gender, number, and case.

Here:

• bíllinn is masculine
• singular
• nominative

So the adjective must also be in the masculine singular nominative form:

• hraður

Other forms include:

• hröð for some feminine/neuter forms
• hratt for neuter singular nominative/accusative and also as an adverb in many contexts

So hraður is the correct matching form for bíllinn.

You usually learn the gender along with the noun. In dictionaries, Icelandic nouns are normally marked as m., f., or n.

• bíll is masculine
• therefore: bíllinn
• and the adjective becomes hraður

There are some patterns that help, but they are not completely reliable, so it is best to memorize nouns with their gender.

Er is the present tense of the verb vera, which means to be.

So:

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

In Bíllinn er hraður, er simply means is.

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

• Bíllinn = subject
• er = verb
• hraður = predicate adjective

So it follows the pattern:

The car + is + fast

That said, Icelandic word order can be more flexible than English in other sentence types, especially because Icelandic has a richer case system.

Because Icelandic usually expresses the by attaching it to the noun:

• hús = house
• húsið = the house
• bíll = car
• bíllinn = the car

There is also a separate demonstrative-like form in Icelandic that can sometimes function similarly, but for ordinary the, the suffixed article is the normal choice.

A rough guide for an English speaker is:

• Bíllinn ≈ BEET-lin or BEEL-lin
• er ≈ ehr
• hraður ≈ HRAA-thur or HROW-thur, depending on how detailed you want to get

A few useful pronunciation notes:

• í is a long ee-like sound
• ll in Icelandic is not always pronounced like English ll; in many contexts it has a special Icelandic sound
• ð is like the th in this, not the th in thin
• hr begins with a voiceless r-type sound; learners often approximate it simply as hr

A beginner-friendly pronunciation is fine at first; native-like pronunciation takes time.

Because hraður is not being used directly before the noun as an attributive adjective. It is being used as a predicate adjective after the verb to be.

Compare:

• hraður bíll = a fast car
  Here the adjective comes directly before the noun.

• Bíllinn er hraður = The car is fast
  Here the adjective comes after er because it describes the subject through the verb is.

This works much like English.

No. That is not the correct form for this meaning.

If you want to say the fast car, you would say:

• hraði bíllinn? No, that is still not right.

The correct form is:

• hraði bíll = not correct for fast car
• hraður bíll = a fast car
• hraði is actually a noun meaning speed

So:

• hraður bíll = a fast car
• bíllinn er hraður = the car is fast

The adjective form you want here is hraður, not hraði.

Usually it means fast, quick, or rapid, depending on context.

With bíllinn, it naturally means the car moves fast. But in other contexts, related forms can describe quick actions, fast processes, and so on.

As always, the exact English translation depends on context, but fast is the most natural meaning here.

It is in the nominative case because it is the subject of the sentence.

In Bíllinn er hraður:

• bíllinn = subject → nominative
• hraður agrees with it in nominative as a predicate adjective

This is one reason Icelandic adjective endings change: case matters.

Yes. In Icelandic, both can change depending on grammar.

For example, when case, number, or definiteness changes, the forms may also change. The exact patterns depend on the noun class and adjective declension.

That means you do not just learn:

• bíll = car
• hraður = fast

You eventually learn a set of forms such as:

• bíll, bíl, bíls, bílum, etc.
• hraður, hraðan, hröðum, and so on

At first, the important thing is to notice that Icelandic grammar uses endings much more actively than English.