Learn Hardcore Icelandic: Bensínið kostar mikið.

bensínið is the definite singular form of the neuter noun bensín (petrol/gasoline). Icelandic marks the definite article by suffixing it to the noun:

bensín = “petrol” (indefinite)
bensínið = “the petrol” (definite; -ið is the neuter‐singular article)

Is mikið an adjective describing bensínið, or something else? Why doesn’t it agree in gender and case?

Here, mikið is an adverb modifying the verb kostar (“costs”). It means “a lot” or “much” and never changes form. If you wanted an adjective meaning “expensive,” you would use dýr (e.g. Bíllinn er dýr – “The car is expensive”).

Why is the verb kosta written as kostar here?

kosta means “to cost.” In the present tense it conjugates as:
• ég kosta
• þú kostar
• hann/hún/það kostar
• við kostum
• þið kostið
• þeir/þær/þau kosta
Since bensínið is 3rd person singular, we use kostar.

Could I say Bensínið er dýrt instead of Bensínið kostar mikið? Are they interchangeable?

Yes.
• Bensínið er dýrt = “The petrol is expensive.” (uses the adjective dýr)
• Bensínið kostar mikið = “The petrol costs a lot.” (uses the verb kosta + adverb mikið)
Both express high cost; the former states a quality, the latter focuses on the amount you pay.

How do I ask “How much does the petrol cost?” in Icelandic?

Use hvað (“what/how much”) + verb + subject:
Hvað kostar bensínið?
Literally “What costs the petrol?” but idiomatically “How much does the petrol cost?”

How can I specify the price per unit, for example “per litre”?

Use á + the dative singular of the unit. For example:
Bensínið kostar 150 krónur á lítra.
– 150 krónur = “150 crowns (ISK)”
– á = preposition “at/on,” which governs the dative
– lítra = dative singular of lítri (“litre”)
So you get “The petrol costs 150 ISK per litre.”