Basilíkan er í gróðurhúsinu.

Basilíka is the basic noun, meaning basil. The ending -n is the suffixed definite article, so basilíkan means the basil.

It is also in the nominative singular, because it is the subject of the sentence.

Because í takes different cases depending on meaning.

Here it shows location, so it takes the dative: í gróðurhúsinu = in the greenhouse

The form gróðurhúsið is the nominative/accusative definite singular. You would use that form with í when the meaning is movement into something, for example: Ég set basilíkuna í gróðurhúsið = I put the basil into the greenhouse.

It can mean either, depending on the case:

• í + dative = in, inside a place
• í + accusative = into, to a place

In your sentence, gróðurhúsinu is dative, so the meaning is in the greenhouse, not into the greenhouse.

Er means is. It is the 3rd person singular present tense of the verb vera = to be.

Because basilíkan is singular, er is the correct form. If the subject were plural, you would usually use eru.

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

So:

• basilíka = basil
• basilíkan = the basil

And:

• gróðurhús = greenhouse
• gróðurhúsinu = in the greenhouse after the right case ending is added

The exact article ending changes with gender, number, and case.

Basilíka is feminine.
Gróðurhús is neuter.

That matters because Icelandic changes noun forms based on gender, number, and case. So the endings are different:

• feminine nominative definite singular: basilíkan
• neuter dative definite singular: gróðurhúsinu

This is one reason Icelandic nouns often look quite different depending on their role in the sentence.

Yes. The sentence as written is the most neutral order:

Basilíkan er í gróðurhúsinu.

But you can also front the location phrase for emphasis or context:

Í gróðurhúsinu er basilíkan.

That is still natural Icelandic. In main clauses, Icelandic usually keeps the finite verb early in the sentence, following the verb-second pattern.

In this sentence, basilíkan most naturally refers to a specific basil plant or the basil already known in the conversation.

English often uses basil without the, but Icelandic basilíkan sounds more specific. If you meant basil more generally, you would usually choose a different form or phrasing without the definite article.

Yes. It is made from:

• gróður = growth, vegetation, plant life
• hús = house

So gróðurhús is literally something like growth-house, which corresponds nicely to greenhouse. Icelandic uses compound words very often, so spotting the parts can help a lot with vocabulary.

A rough English-friendly guide is:

• basilíkan: BA-si-lee-kan
• gróðurhúsinu: GRO-thur-hoo-si-nu

A few useful notes:

• Stress is usually on the first syllable in Icelandic.
• í sounds like ee.
• ð sounds like the th in this.

These are only approximations, but they are a good starting point.