Barnið fær snarl eftir skóla.

Fá is the infinitive, meaning to get or to receive.
Fær is the present-tense form used with a third-person singular subject like barnið.

A few forms of fá are:

• ég fæ = I get
• þú færð = you get
• hann / hún / það fær = he / she / it gets

So barnið fær means the child gets.

Because Icelandic has no indefinite article. English uses a/an, but Icelandic usually just uses the noun by itself.

So:

• snarl = a snack
• snarlið = the snack

It is the direct object of fær, and the verb fá normally takes the accusative. In this sentence, snarl is accusative singular.

The reason that may not look obvious is that for this noun, the accusative singular looks the same as the basic dictionary form.

Because eftir is a preposition, and prepositions require certain cases. In a time expression like after school, eftir takes the accusative, so skóli becomes skóla.

So:

• skóli = school
• eftir skóla = after school

Eftir skóla is a standard general expression meaning after school, much like in English. It refers to the usual routine or time of day, not necessarily to one specific school as a definite object.

That is why Icelandic naturally uses skóla here rather than a definite form.

Yes. Icelandic word order is more flexible than English word order, but in a main clause the finite verb usually stays in the second position.

So both of these are natural:

• Barnið fær snarl eftir skóla.
• Eftir skóla fær barnið snarl.

The second version gives more emphasis to after school. What you normally cannot do is move eftir skóla to the front and leave the verb later: Eftir skóla barnið fær snarl is not standard word order.