Hundurinn er inni í bílnum.

Because hundurinn means the dog, while hundur means a dog or just dog.

In Icelandic, the definite article is usually attached to the end of the noun instead of being a separate word like English the.

• hundur = dog
• hundurinn = the dog

So the sentence starts with a definite subject: the dog.

Hundurinn is in the nominative singular.

That is the case normally used for the subject of a sentence, and here the dog is the subject of er.

A simple way to see it:

• hundur = nominative singular indefinite
• hundurinn = nominative singular definite

So Icelandic is marking both:

• number: singular
• gender: masculine
• definiteness: definite
• case: nominative

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

Here it means is.

Because hundurinn is third person singular, Icelandic uses er:

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

So Hundurinn er ... = The dog is ...

Yes, to an English speaker it can look a bit repetitive at first.

Here is the difference:

• inni is an adverb meaning inside
• í is a preposition meaning in or into, depending on context

So inni í bílnum is literally something like inside in the car, but naturally it means inside the car.

This combination is very common in Icelandic.
It makes the location especially clear: the dog is physically inside the car, not just at the car or near it.

Because bílnum is the dative singular definite form of bíll.

After í when it describes a location rather than movement, Icelandic uses the dative.

Here the dog is already located in the car, so you get:

• í bílnum = in the car

Useful comparison:

• Hundurinn er í bílnum. = The dog is in the car.
  
  • location, so dative
• Hundurinn fer í bílinn. = The dog goes into the car.
  
  • movement into, so accusative

So the ending in bílnum is there because of both:

• the dative case
• the definite article

Yes, absolutely.

Hundurinn er í bílnum is perfectly normal and natural. It simply means The dog is in the car.

Adding inni makes it a bit more explicit or vivid:

• Hundurinn er í bílnum. = The dog is in the car.
• Hundurinn er inni í bílnum. = The dog is inside the car.

So inni is not always required, but it adds emphasis to the idea of being inside.

Because Icelandic normally expresses the by attaching it to the noun as a suffix.

So instead of having a separate word like English the, Icelandic often does this:

• hundur = dog

• hundurinn = the dog

• bíll = car
• bílnum = in/to the car, with the definite article included

This is one of the big differences between English and Icelandic noun structure.

The dictionary form is bíll, meaning car.

In the sentence, that noun changes form because Icelandic nouns inflect for case and definiteness.

A few useful forms are:

• bíll = car, nominative singular indefinite
• bíl = car, accusative singular indefinite
• bílnum = the car, dative singular definite
• bílinn = the car, accusative singular definite
• bíllinn = the car, nominative singular definite

So bílnum is not a separate vocabulary word you memorize by itself first; it is a form of bíll.

Yes.

The neutral word order here is:

• Hundurinn er inni í bílnum.

That is a very standard subject + verb + location structure.

But Icelandic can move parts of the sentence for emphasis or style. For example:

• Inni í bílnum er hundurinn.
• Í bílnum er hundurinn.

These are possible, but once something other than the subject comes first, Icelandic normally keeps the finite verb in the second position. That is a common Icelandic word-order pattern.

So the original sentence is the most straightforward version, but it is not the only possible one.

Not always.

You can often just use í with a place noun:

• í húsinu = in the house
• í bílnum = in the car

But inni is often added when the speaker wants to stress that something is inside rather than outside. It is especially common in everyday speech.

So:

• í bílnum = in the car
• inni í bílnum = inside the car

Both are good Icelandic; the second is just more explicit.