Barnið gengur í rigningunni í nýju regnstígvélunum sínum og hlær hátt.

Barn means child in an indefinite sense. Barnið means the child.

Icelandic usually adds the definite article to the end of the noun instead of putting a separate word before it. So the ending -ið here is basically the attached to barn.

Also, barn is a neuter noun, and barnið is its nominative/accusative singular definite form.

Yes. Icelandic very often makes compound nouns by writing them as a single word.

Here:

• regn = rain
• stígvél = boot / boots

So regnstígvél means rain boot or rain boots. In the sentence, the form regnstígvélunum is dative plural definite: the rain boots.

Because both phrases use the idea of in:

• í rigningunni = in the rain
• í nýju regnstígvélunum sínum = literally in his/her own new rain boots

That second use may feel unusual to an English speaker, because English often prefers wearing boots, but Icelandic commonly uses í with clothing and footwear.

Because í takes:

• dative for location or state
• accusative for motion into something

Here, the child is walking in the rain and in the boots, not moving into them, so both phrases are in the dative.

A useful contrast is:

• í húsinu = in the house → location, so dative
• í húsið = into the house → motion into, so accusative

Even though gengur is a motion verb, the prepositional phrases here describe the setting, not a destination.

The base noun is rigning, a feminine noun meaning rain or rainfall.

In í rigningunni:

• rigning- = the noun stem
• -unni = dative singular definite ending

So rigningunni means the rain in the dative singular.

Because the phrase is definite: in the new rain boots.

In Icelandic, when the noun is definite, the adjective usually takes the weak form. That is why you get:

• í nýju regnstígvélunum = in the new rain boots

If the phrase were indefinite, you would use the strong adjective and the noun without the definite article:

• í nýjum regnstígvélum = in new rain boots

So the difference is:

• nýju regnstígvélunum = the new rain boots
• nýjum regnstígvélum = new rain boots

Because sinn / sín / sitt is the reflexive possessive in Icelandic.

You use it when the possessor is the same as the subject of the clause. Here, the subject is barnið, and the boots belong to that same child, so Icelandic uses sínum.

So:

• í regnstígvélunum sínum = in his/her own rain boots

If the boots belonged to someone else, you would use a non-reflexive possessive such as:

• hans = his
• hennar = her
• þeirra = their

Because sínum agrees with the thing possessed, not with the owner.

Here it agrees with regnstígvélunum, which is:

• dative
• plural

So the possessive must also be dative plural: sínum.

Also, barnið is grammatically neuter because barn is a neuter noun. That is grammatical gender, not necessarily the child’s real-world gender.

That is very normal in Icelandic.

English often puts possessives before the noun, as in his boots, but Icelandic very often places possessive pronouns after the noun, especially in ordinary prose:

• regnstígvélunum sínum = literally the rain boots own/his/her

So the word order may look backward from an English perspective, but it is standard Icelandic.

Because both verbs share the same subject: barnið.

So:

• Barnið gengur ... og hlær hátt

  means:

• The child walks ... and laughs loudly

Icelandic, like English, does not need to repeat the subject when two verbs are joined this way and the subject is clearly the same.

Here hátt functions as an adverb, meaning loudly.

In Icelandic, adverbial meanings are often expressed with a form related to an adjective. In this case, hátt is the form used in expressions like:

• hlæja hátt = laugh loudly
• tala hátt = speak loudly

So although it may look adjective-like to an English learner, in this sentence it is simply the normal adverbial form.

They are both present tense, 3rd person singular:

• gengur = from ganga
• hlær = from hlæja

A useful point for English speakers is that Icelandic often uses the simple present where English might use either the simple present or the present progressive. So depending on context, these forms can mean:

• walks or is walking
• laughs or is laughing

Also, hlæja has a form that learners often just need to memorize: hann/hún/það hlær.