Barnið fær kex og smá gos eftir kvöldmat, ef það hefur verið að leika sér úti allan daginn.

Barnið means the child. The noun barn is neuter, and Icelandic usually adds the definite article to the end of the noun, so:

• barn = a child / child
• barnið = the child

Here it is the subject of the sentence, so it is in the nominative singular.

Fær is the 3rd person singular present tense of að fá = to get / receive.

Because the subject is barnið (the child), the verb has to match that subject:

• ég fæ = I get
• þú færð = you get
• barnið fær = the child gets

In this sentence, the present tense can describe a general rule or usual outcome, not just something happening right now.

They are the direct objects of fær, so they are in the accusative.

But their forms do not obviously change here:

• kex is often treated as an indeclinable noun
• gos is a neuter noun whose nominative and accusative singular are the same in this form

So even though the grammar calls for accusative, the words still look the same.

Here smá means a little / some. In everyday Icelandic, smá is very often used as an indeclinable modifier, especially before mass nouns or uncountable things like gos.

So smá gos means a little soda / some soda.
Even though many Icelandic adjectives do change for gender, number, and case, smá often stays the same in this common use.

Because the preposition eftir means after here, and in this meaning it takes the accusative.

The dictionary form is:

• kvöldmatur = dinner / evening meal

But the accusative singular is:

• kvöldmat

So eftir kvöldmat = after dinner.

Because barn is a neuter noun, and Icelandic pronouns usually agree with the grammatical gender of the noun they refer to.

So:

• barnið is neuter
• therefore the matching pronoun is það

This is normal grammar in Icelandic. It does not automatically sound rude. If the speaker wants to refer to a specific child as a boy or girl, they might also use hann or hún in some contexts, but það is perfectly natural with barnið.

Ef means if and introduces a subordinate clause:

• ef það hefur verið að leika sér úti allan daginn

In this kind of clause, Icelandic does not use main-clause verb-second word order in the same way. So the structure is straightforward:

• ef
  • subject + verb
• ef það hefur...

That is why you see það hefur verið..., not hefur það verið...

This is a very common Icelandic way to express something like has been playing.

It is built like this:

• hefur = has
• verið = been
• að leika sér = playing / to be playing

So hefur verið að leika sér means has been playing or has been busy playing.

The pattern vera að + infinitive often expresses an ongoing action, somewhat like English be doing. With hefur verið að..., it becomes has been doing...

Because að leika sér is the normal Icelandic expression for to play in the sense of children playing.

The word sér is a reflexive pronoun. In this phrase, it is just part of how the verb is used. So you should learn:

• leika sér = play

Without sér, leika often has a different meaning, such as play/perform something, act, or play a role.

Because úti means outside / outdoors, describing location.

• úti = outside, outdoors
• út = out, outward, to the outside

Here the meaning is that the child has been playing outside, not moving outward at that moment. So úti is the right choice.

Allan daginn is in the accusative, and it expresses duration of time: all day.

Breakdown:

• dagurinn = the day
• daginn = the day (accusative)
• allur = all
• allan = all (masculine accusative singular, matching daginn)

Using the accusative for length of time is very common in Icelandic, so allan daginn means for the whole day / all day.

Because the sentence is describing a general rule or repeated situation:

• the child gets crackers and a little soda
• if it has been playing outside all day

So fær is present tense because it expresses what usually happens in that situation. English does something similar in sentences like If he has been good, he gets dessert.

Yes — several very useful Icelandic patterns appear here:

• X fær Y = X gets Y
• eftir + accusative = after something
• ef + clause = if ...
• hafa verið að + infinitive = have been doing ...
• leika sér = play
• accusative of time duration: allan daginn = all day

If you learn those chunks as patterns, sentences like this become much easier to build and understand.