Hún leitar að bangsanum sínum undir teppinu.

A word-by-word breakdown is:

• Hún = she
• leitar = looks / is looking / searches
• að bangsanum sínum = for her own teddy bear
• undir teppinu = under the blanket

So grammatically, it is:

• subject: Hún
• verb: leitar
• object phrase with the verb: að bangsanum sínum
• location phrase: undir teppinu

Because Icelandic often uses the simple present where English uses either:

• she looks for
• she is looking for

So Hún leitar can mean either one, depending on context.

If you want to make the ongoing action extra explicit, Icelandic can also say:

• Hún er að leita að bangsanum sínum.

That is closer to English She is looking for her teddy bear.

Here, að is part of the fixed verb expression leita að, which means to look for or to search for.

So you should learn:

• leita að einhverju = look for something

In this sentence, að is not the infinitive marker to. It belongs with the verb.

Because bangsi has to change form here.

The base form is:

• bangsi = teddy bear

But after leita að, the noun normally goes in the dative. Also, this is a specific teddy bear, so the noun is definite.

That gives:

• bangsanum = the teddy bear in the dative singular

So:

• að bangsanum = for the teddy bear

Because Icelandic uses the reflexive possessive sinn / sín / sitt when the owner is the same as the subject of the sentence.

Here:

• subject = Hún
• owner of the teddy bear = the same she

So Icelandic uses sínum:

• bangsanum sínum = her own teddy bear

If you said bangsanum hennar, that would usually mean the teddy bear belongs to some other female person, not to the subject herself.

Because sinn has to agree with the noun it describes.

The noun is:

• bangsanum
• masculine
• singular
• dative

So the matching form is:

• sínum

This agreement is with the possessed noun, not directly with the person doing the possessing.

That is a normal Icelandic pattern.

In Icelandic, possessives often come after the noun:

• bókin mín = my book
• húsið okkar = our house
• bangsanum sínum = her own teddy bear

And the noun is often definite at the same time. English usually does not do this, but Icelandic often does.

So even though English says:

• her teddy bear

Icelandic naturally says something more like:

• the teddy bear her-own

That is just standard Icelandic structure.

The base noun is:

• teppi = blanket

Here it appears after undir in a location sense, so it goes in the dative. It is also definite, so:

• teppinu = the blanket in the dative singular

So:

• undir teppinu = under the blanket

No. Undir can take different cases depending on meaning.

A very common rule is:

• dative = location, being somewhere
• accusative = motion toward a place

So:

• undir teppinu = under the blanket (location)
• undir teppið = to under the blanket / under the blanket as a destination

In this sentence, the meaning is location, so dative is used.

Usually, yes. In everyday Icelandic, bangsi commonly means a teddy bear or stuffed bear, especially in child-related contexts.

It has a warm, childlike feel, similar to English teddy or teddy bear.

That is a very natural place for a location phrase in Icelandic.

The sentence follows a common pattern:

• subject
• verb
• object/complement
• place phrase

So:

• Hún
• leitar
• að bangsanum sínum
• undir teppinu

You can move parts of the sentence for emphasis, but Icelandic main clauses usually keep the finite verb in second position. For example:

• Undir teppinu leitar hún að bangsanum sínum.

That is still grammatical, but it gives more emphasis to under the blanket.