Hún útvegaði honum lykil.

Because útvega normally takes:

• a dative person = the person who receives or benefits
• an accusative thing = the thing provided

So in Hún útvegaði honum lykil, honum is the dative form of hann and means to him / for him.

A useful pattern to memorize is:

• útvega einhverjum eitthvað = to provide someone with something

So:

• einhverjum = dative
• eitthvað = accusative

Because lykill is the dictionary form, but here the noun is in the accusative singular.

The noun changes like this:

• lykill = nominative singular
• lykil = accusative singular

That happens because lykill is the direct object of the verb útvegaði.

So:

• Hún = subject
• útvegaði = verb
• honum = indirect object / dative recipient
• lykil = direct object / accusative thing

Útvegaði is the past tense, 3rd person singular of útvega.

So it matches the subject hún = she.

A few examples:

• ég útvegaði = I provided
• þú útvegaðir = you provided
• hún útvegaði = she provided

The ending -ði is a common past-tense ending for weak verbs in Icelandic.

Because Icelandic does not have a separate indefinite article like English a/an.

So:

• lykill can mean a key or just key, depending on context
• lykil here means a key in natural English translation

If you wanted the key, Icelandic usually adds the definite article to the end of the noun:

• lykilinn = the key (accusative singular)

So compare:

• Hún útvegaði honum lykil. = She provided him with a key.
• Hún útvegaði honum lykilinn. = She provided him with the key.

Hún is the subject pronoun, meaning she.

It is in the nominative, because the subject of the sentence is normally nominative in Icelandic.

So the basic structure is:

• Hún = she
• útvegaði = provided
• honum = to him / for him
• lykil = a key

Mostly yes in this sentence, but the grammar behind it is more case-based.

The order here is:

• Subject + Verb + Indirect Object + Direct Object

So:

• Hún (subject)
• útvegaði (verb)
• honum (indirect object)
• lykil (direct object)

This is a very natural Icelandic order, especially when the indirect object is a short pronoun like honum.

However, Icelandic word order is generally more flexible than English because case endings show what each word is doing.

Yes. In terms of structure, Icelandic allows the equivalent of provided him a key, but in natural English the best translation is usually provided him with a key or got him a key.

The important grammar point is that Icelandic uses:

• dative for the person: honum
• accusative for the thing: lykil

So even if English needs a preposition like with or for, Icelandic often expresses that relationship just through case.

Very often, yes. A common pattern is:

• útvega einhverjum eitthvað

That means:

• provide someone with something
• get something for someone
• procure something for someone

So if you learn this verb, it is best to learn it together with its case pattern, not just as a simple dictionary meaning.

For example:

• Hún útvegaði honum vinnu. = She got him a job.
• Þeir útveguðu mér bíl. = They got me a car.

This is a good habit for Icelandic in general: learn verbs together with the cases they require.

Because that is the normal and very natural order here, especially when the recipient is a short pronoun.

In Icelandic, when you have both objects after the verb, a pronoun indirect object often comes before the direct object:

• útvegaði honum lykil

That sounds smooth and neutral.

Different word orders are sometimes possible for emphasis or style, but this version is the one most learners should treat as the default pattern.

A rough pronunciation guide is:

• út-ve-ga-thi or oot-ve-ga-thi

A few notes:

• ú is like oo in food
• g here is softer than English g in many contexts
• ð is like the th in this, but in some positions Icelandic speakers pronounce it quite lightly
• the stress is normally on the first syllable: ÚTvegaði

You do not need to pronounce the ð like a hard d. It is usually a soft sound.

A very useful chunk is:

• Hún útvegaði honum lykil.
• útvega einhverjum eitthvað

From this one sentence, you can learn all of these:

• hún = nominative subject form of she
• útvegaði = past tense of útvega
• honum = dative of hann
• lykil = accusative of lykill

So the sentence is a great example of how Icelandic uses case endings instead of extra prepositions or fixed English-style word order.