Garðaúrgangurinn er í bílnum.

Icelandic makes a lot of compound nouns, much more freely than English.

Garðaúrgangurinn breaks down like this:

• garða- = a compound form related to garður (garden)
• úrgangur = waste
• -inn / surface form -urinn = the

So the base noun is garðaúrgangur = garden waste, and garðaúrgangurinn = the garden waste.

This kind of long compound is very normal in Icelandic.

Because Icelandic often uses a genitive form in compounds.

Here, garða- comes from garða, the genitive plural of garður (garden). So the compound literally looks something like waste of gardens, which English expresses more naturally as garden waste.

This is a very common pattern in Icelandic compound words. You do not always translate that internal genitive literally; it is just part of how the compound is built.

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

So:

• garðaúrgangur = garden waste
• garðaúrgangurinn = the garden waste

And:

• bíll = car
• bílnum = the car in a particular case form

There is a separate article in Icelandic (hinn / hin / hið), but in an ordinary sentence like this, the suffixed article is the normal choice.

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

In Garðaúrgangurinn er í bílnum, the thing being talked about is the garden waste, so that noun is the subject, and Icelandic subjects are normally in the nominative.

So:

• Garðaúrgangurinn = nominative singular definite
• it matches its role as the thing that is in the car

Because the preposition í can take different cases depending on meaning.

Here it means in in the sense of location: the garden waste is already inside the car. With that meaning, í takes the dative.

So:

• dictionary form: bíll = car
• dative singular definite: bílnum = the car

That is why the sentence has í bílnum.

This is a very important Icelandic pattern:

• í + dative = in / inside, showing location
• í + accusative = into, showing movement toward the inside

So:

• í bílnum = in the car (already there)
• í bílinn = into the car (movement into it)

In your sentence, the meaning is location, so í bílnum is correct.

Er is the present-tense singular form of vera, the verb to be.

So here:

• Garðaúrgangurinn er í bílnum = The garden waste is in the car

It works very much like English is in this sentence.

Both garðaúrgangur and bíll are masculine nouns, and yes, that matters a lot.

In Icelandic, gender affects:

• the form of the definite article
• case endings
• adjective agreement

That is part of why you get forms like:

• garðaúrgangurinn rather than some other definite form
• bílnum in the dative singular definite

So when learning Icelandic nouns, it is best to learn each noun together with its gender.

Yes, but the sentence as given is the most neutral order:

• Garðaúrgangurinn er í bílnum.

You can also move the location to the front for emphasis:

• Í bílnum er garðaúrgangurinn.

That sounds more like In the car is the garden waste or The garden waste is in the car with extra focus on the location.

This also shows an important Icelandic rule: in main clauses, the finite verb is usually in second position.

Yes, grammatically you can, but the meaning changes.

• Garðaúrgangurinn er í bílnum = The garden waste is in the car
• Garðaúrgangur er í bílnum = Garden waste is in the car / There is garden waste in the car

Without the article, the noun is indefinite or more general.

In natural Icelandic, if you want to say There is garden waste in the car, you would often say:

• Það er garðaúrgangur í bílnum.

So dropping the article is possible, but it changes how the sentence sounds and what it emphasizes.