Barnið tekur um höndina mína þegar við förum út.

Barnið is the definite form of barn, so it means the child rather than just child.

• barn = child
• barnið = the child

Icelandic usually adds the definite article to the end of the noun instead of using a separate word like English the.

No. This is grammatical gender, not biological sex.

The noun barn is grammatically neuter, so it always behaves like a neuter noun in Icelandic, no matter whether the child is a boy or a girl.

Tekur is the 3rd person singular present form of the verb taka.

That matches the subject barnið, which is singular:

• ég tek = I take
• þú tekur = you take
• hann/hún/það tekur = he/she/it takes

So Barnið tekur... means The child takes...

Here taka um is a natural Icelandic expression meaning something like take hold of or grasp, especially around a body part.

So tekur um höndina mína is the Icelandic way of expressing takes my hand or takes hold of my hand.

It is not a word-for-word match with English, but it is idiomatic Icelandic.

Because um takes the accusative case, and in this sentence höndina is the noun after um.

• höndin = the hand, nominative
• höndina = the hand, accusative

So after um, you need höndina.

Mína is the form of minn meaning my, and it must agree with höndina in gender, number, and case.

Since höndina is:

• feminine
• singular
• accusative

the possessive must also be:

• feminine
• singular
• accusative

So you get mína.

A useful mini-pattern is:

• minn = masculine
• mín = feminine
• mitt = neuter

and the case endings then change from there.

That is a very common Icelandic pattern.

With a definite noun, Icelandic often places the possessive after the noun:

• höndina mína = my hand

This is more natural and neutral in everyday Icelandic than putting the possessive first.

A fronted version like mín hönd is possible, but it is usually more emphatic, contrastive, or literary in tone.

Because Icelandic usually uses a suffixed definite article.

Instead of a separate word like English the, Icelandic often adds the article to the noun itself:

• barn → barnið
• hönd → höndin / höndina

So the idea of the is built into the noun form.

That is a good question. Icelandic is a verb-second language in main clauses, but þegar við förum út is a subordinate clause introduced by þegar.

In subordinate clauses, normal subject + verb order is common:

• þegar við förum út = when we go out

So við comes before förum here.

Because fara is an irregular verb and its forms change quite a bit.

The present tense is:

• ég fer
• þú ferð
• hann/hún/það fer
• við förum
• þið farið
• þeir/þær/þau fara

So förum is simply the correct 1st person plural present form: we go.

Út means out or outside, and with fara it forms the very common expression fara út:

• fara út = go out / go outside

So við förum út means we go out or we go outside.

Here it means when.

That is because it introduces a whole clause:

• þegar við förum út = when we go out

The word þegar can also mean already in other contexts, but not in this sentence.