Hún ver basilíkuna með því að rækta hana í gróðurhúsinu.

Ver here means protects or defends. It is the 3rd person singular present form of the verb verja.

So:

• að verja = to protect, defend
• hún ver = she protects

A learner might mistake ver for something related to vera (to be), but it is a different verb.

Because basilíkuna is:

• singular
• definite = the basil
• accusative

The base noun is basilíka. In this sentence it is the direct object of ver, and verja takes the accusative.

A rough breakdown is:

• basilíka = basil
• basilíkuna = the basil

So the ending tells you both that it is definite and that it is in the accusative case.

Hana is needed because rækta also needs its own object: grow/cultivate it.

In English, we also usually repeat the object:

• She protects the basil by growing it in the greenhouse.

We do not normally say:

• She protects the basil by growing in the greenhouse
  unless we mean growing things in general.

So hana refers back to basilíkuna and means it.

Because basilíka is a feminine noun in Icelandic.

In Icelandic, pronouns agree with the grammatical gender of the noun they refer to. So even though English uses it, Icelandic uses the feminine form because the noun is feminine.

Here:

• basilíka = feminine noun
• hana = accusative singular feminine pronoun

So hana means it, but grammatically it is feminine.

Með því að is a very common Icelandic expression meaning by doing something.

So:

• með því að rækta hana = by growing it

It is best to learn með því að as a fixed phrase. Word-for-word it is not very natural in English, but functionally it introduces the method or means by which something happens.

Examples:

• Hann lærir með því að lesa. = He learns by reading.
• Hún hjálpar með því að kenna. = She helps by teaching.

Because rækta is in the infinitive after the expression með því að.

So the structure is:

• með því að + infinitive

Examples:

• með því að lesa = by reading
• með því að skrifa = by writing
• með því að rækta = by growing/cultivating

This is the normal pattern.

Because rækta means to cultivate / to grow something.

This is an important distinction in Icelandic:

• rækta = to grow/cultivate something
  
  • Hún ræktar basilíku. = She grows basil.
• vaxa = to grow, in the sense of becoming bigger or growing by itself
  
  • Basilíkan vex. = The basil grows.

So in this sentence, the subject is actively caring for the plant, so rækta is the right verb.

Because gróðurhúsinu is:

• definite = the greenhouse
• singular
• dative

The noun is gróðurhús (greenhouse), which is a neuter noun.

After í, Icelandic uses:

• dative for location: in
• accusative for motion into: into

Here the meaning is location, not movement. She is growing it in the greenhouse, so we get:

• í gróðurhúsinu = in the greenhouse

Compare:

• í gróðurhúsinu = in the greenhouse
• í gróðurhúsið = into the greenhouse

Yes, this is a very natural, neutral word order.

The sentence is basically:

• Hún ver basilíkuna = She protects the basil
• með því að rækta hana í gróðurhúsinu = by growing it in the greenhouse

So the full sentence follows a common pattern:

• subject + verb + object + adverbial phrase

Icelandic word order is somewhat flexible, so other versions are possible for emphasis, such as:

• Með því að rækta hana í gróðurhúsinu ver hún basilíkuna.

But the original sentence is the most straightforward, neutral way to say it.