Hún ber bolla og diska á stórum bakka inn í stofuna.

Bera is the infinitive, meaning to carry / to bear.

Ber is the present tense, 3rd person singular form, used with hún (she):

• ég ber = I carry
• þú berð = you carry
• hún ber = she carries

So Hún ber ... means She carries ...

They are the direct objects of ber, and bera normally takes the accusative case.

So:

• bolli → bolla in the accusative
• diskur → diska in the accusative plural

That is why you get:

• bolla
• diska

Even though English does not change these nouns by case, Icelandic does.

Because á can take either the dative or the accusative, depending on meaning:

• á + dative = location / position on
• á + accusative = movement onto

Here, the cups and plates are on the tray while she is carrying them. The relationship is one of location, not movement onto the tray, so Icelandic uses the dative:

• á bakka = on a tray
• á stórum bakka = on a large tray

If you were talking about putting something onto the tray, accusative would be more likely, for example:

• að setja bolla á bakka / á stóran bakka

Adjectives in Icelandic must agree with the noun they describe in:

• gender
• number
• case

Here, bakki is:

• masculine
• singular
• dative

So the adjective stór has to match that, giving stórum.

That is why you get:

• á stórum bakka

not just a fixed form like English large.

This shows movement into the room.

A very common pattern in Icelandic is:

• inn í + accusative = into
• inni í + dative = in / inside

So:

• inn í stofuna = into the living room
• inni í stofunni = in the living room

Because the sentence describes motion toward the room, Icelandic uses inn í and the accusative form stofuna.

Yes, í stofuna can already mean into the living room in the right context, but inn makes the direction more explicit: inward, into.

So:

• í stofuna = into the living room
• inn í stofuna = more explicitly in into the living room

With rooms, buildings, and enclosed spaces, inn í is very common and sounds very natural.

Because stofuna is the accusative singular definite form of stofa.

• stofa = a living room
• stofan = the living room (nominative)
• stofuna = the living room (accusative)

Since inn í here expresses motion and takes the accusative, the sentence needs stofuna.

So inn í stofuna literally means into the living room.

Icelandic does not normally use a separate indefinite article like English a / an.

So:

• bakki can mean a tray
• bollar can mean cups
• diskar can mean plates / dishes

Indefiniteness is often just left unmarked.

But Icelandic does have a definite article, and it is usually attached to the end of the noun:

• stofa = living room
• stofan / stofuna = the living room

So in this sentence:

• bolla og diska = cups and plates
• á stórum bakka = on a large tray
• í stofuna = into the living room

Yes. This is a very natural word order:

• Hún = subject
• ber = verb
• bolla og diska = object
• á stórum bakka = prepositional phrase
• inn í stofuna = directional phrase

So the sentence is built in a straightforward way: She carries cups and plates on a large tray into the living room.

Icelandic word order is somewhat flexible, but this version is neutral and idiomatic. You can move parts around for emphasis, but this is a standard way to say it.