Krakkarnir eru uppi að leika sér, en foreldrarnir eru niðri í eldhúsinu.

Yes. Krakki means kid, so krakkarnir means the kids.

It is a very common everyday word and sounds natural here. It is a bit more informal than börn (children). So this sentence sounds like normal spoken Icelandic rather than especially formal language.

In Icelandic, the definite article is usually attached to the end of the noun instead of being a separate word.

In this sentence:

• krakkarnir = the kids
• foreldrarnir = the parents
• eldhúsinu = the kitchen / in the kitchen

So the -nir and -inu endings include the idea of the.

Because the sentence has two coordinated clauses:

• Krakkarnir eru uppi að leika sér
• en foreldrarnir eru niðri í eldhúsinu

Each clause needs its own finite verb, and eru is the present plural form of vera (to be).

So:

• krakkarnir eru = the kids are
• foreldrarnir eru = the parents are

They are adverbs of place:

• uppi = up / upstairs
• niðri = down / downstairs

In a house, they very often mean upstairs and downstairs without needing to name the floor explicitly.

So:

• eru uppi = are upstairs
• eru niðri = are downstairs

This is a very common distinction:

• uppi / niðri usually describe location: where someone is
• upp / niður usually describe direction or movement: where someone is going

Compare:

• Krakkarnir eru uppi. = The kids are upstairs.
• Krakkarnir fara upp. = The kids go upstairs.

And:

• Foreldrarnir eru niðri. = The parents are downstairs.
• Foreldrarnir fara niður. = The parents go downstairs.

So in your sentence, uppi and niðri fit because the sentence describes where people are.

This is the common Icelandic pattern vera að + infinitive, which often corresponds to English be doing.

So:

• eru að leika sér = are playing

In this sentence, uppi is inserted between eru and að leika sér:

• eru uppi að leika sér

That is perfectly normal. Icelandic often places adverbs in that position. The whole phrase means are upstairs playing.

Because leika sér is the normal expression for to play in the sense of children playing or someone amusing themselves.

So:

• leika sér = play
• leika by itself often has other meanings, such as play/perform/act out

That makes að leika sér the natural choice here for playing.

Sér is a reflexive pronoun, here meaning something like oneself or themselves.

So leika sér is literally something like play oneself, but you should learn it as a fixed Icelandic expression meaning simply play.

A useful thing to know is that in the 3rd person, the reflexive forms do not change for singular vs. plural:

• sig = accusative
• sér = dative
• sín = genitive

So even though krakkarnir is plural, sér is still correct.

Yes. The singular is foreldri (parent), but the plural is foreldrar (parents), and the definite plural is foreldrarnir (the parents).

So the pattern is:

• foreldri = a parent
• foreldrar = parents
• foreldrarnir = the parents

This is one of those Icelandic nouns whose plural does not look exactly like you might first expect from the singular, so it is worth memorizing.

Because í can take different cases depending on whether it shows:

• location → usually dative
• motion into something → usually accusative

Here the parents are already in the kitchen, so this is location:

• í eldhúsinu = in the kitchen

If someone were moving into the kitchen, you would typically get accusative instead:

• fara í eldhúsið = go into the kitchen

So the form eldhúsinu shows location, which matches the sentence.

Yes, Icelandic has some flexibility here.

The given sentence:

• Krakkarnir eru uppi að leika sér

is very natural and brings in the location early: The kids are upstairs playing.

You could also hear:

• Krakkarnir eru að leika sér uppi

That would still be understandable and natural, but the rhythm and emphasis are slightly different. The version in your sentence foregrounds where they are a bit sooner.

So the placement is not random, but it is also not the only possible word order.