Hún hlustaði á símsvarann sinn í strætó og heyrði að ný skilaboð voru líka komin á talhólfið.

They are close in meaning, but not the same.

• hlusta á = to listen to, meaning you do it deliberately
• heyra = to hear, meaning you perceive a sound

So:

• Hún hlustaði á símsvarann sinn = she listened to her answering machine / voicemail
• og heyrði að... = and heard that...

A native English speaker can think of it as the same difference as listen vs hear in English.

The verb hlusta normally takes the preposition á in Icelandic.

So Icelandic says:

• hlusta á tónlist = listen to music
• hlusta á kennarann = listen to the teacher
• hlusta á símsvarann = listen to the answering machine

This is just how the verb works. Unlike English, where listen takes to, Icelandic uses á here.

Because símsvarann is the accusative singular definite form of símsvari.

Here is the idea:

• símsvari = an answering machine / voicemail system
• símsvarinn = the answering machine
• símsvarann = the answering machine, as a direct object

Since hlusta á takes the accusative, the noun changes form:

• á símsvarann

The ending -ann is a common masculine singular definite accusative ending.

Because sinn is the reflexive possessive. It refers back to the subject of the clause, which is hún.

So:

• símsvarann sinn = her own answering machine
• símsvarann hennar would usually suggest someone else’s answering machine, or at least not the reflexive her own meaning

This is a very important Icelandic pattern:

• Hún tók bókina sína. = She took her own book.
• Hún tók bókina hennar. = She took her book, meaning another woman’s book.

Also, sinn agrees with the thing possessed, not with the owner. Since símsvarann is masculine singular accusative, the form is sinn.

í strætó means on the bus or more literally in the bus.

Icelandic often uses í for being inside a vehicle:

• í bíl = in a car
• í lest = on/in a train
• í strætó = on the bus

So even though English usually says on the bus, Icelandic says í strætó.

Also, strætó is very commonly used as a general word for a city bus, so the phrase í strætó is a very normal everyday expression.

They are related, but not exactly identical.

• símsvari usually means an answering machine or answering service
• talhólf means a voicemail box or the place where the messages are stored

So in this sentence, she is listening to the answering system, and she hears that new messages have also arrived in the voicemail box.

In real usage, the distinction can sometimes be a little loose, but that is the basic difference.

Yes. skilaboð is treated as grammatically plural here, so the verb is plural:

• voru = were

That is why you get:

• ný skilaboð voru... = new messages were...

The adjective ný is also correct here. It is the proper form for neuter plural nominative/accusative.

So the agreement is:

• ný = adjective agreeing with neuter plural skilaboð
• voru = plural verb agreeing with skilaboð

This is a very useful Icelandic pattern.

• komu líka = also arrived; this focuses more directly on the event
• voru líka komin = had also arrived / were also already there; this emphasizes the resulting state

So ný skilaboð voru líka komin á talhólfið suggests that the new messages had already arrived and were now there in the voicemail box.

Also, komin agrees with skilaboð:

• kominn = masculine singular
• komin = neuter plural here

This kind of vera + past participle/adjectival participle construction is very common in Icelandic.

komin is the participial/adjectival form related to koma = to come / to arrive.

In this sentence it works with voru:

• voru komin = had come / had arrived / were there already

A helpful way to think of it is that Icelandic often uses these forms almost like adjectives, so they agree with the noun they describe.

Since skilaboð is neuter plural, the form is komin.

Because á often takes:

• accusative for movement toward a destination
• dative for location

Here the messages are understood as arriving onto / into the voicemail box, so Icelandic uses the accusative:

• á talhólfið

Compare the general pattern:

• movement: fara á borðið = go onto the table
• location: vera á borðinu = be on the table

So here the idea is destination: the messages came onto/into the voicemail box.

Here að means that and introduces a subordinate clause.

So:

• heyrði að ný skilaboð voru... = heard that new messages were...

This is also why the word order is what it is. In the að-clause, Icelandic uses normal subordinate-clause word order:

• ný skilaboð voru líka komin...

You do not put the verb first there the way Icelandic often does in main clauses.

líka means also / too, and its position is fairly natural here.

• ný skilaboð voru líka komin = new messages had also arrived

Icelandic adverbs often appear around the finite verb and participle area, so voru líka komin sounds very normal.

If you move líka, the sentence may still be possible, but the emphasis changes slightly. In this sentence, the placement makes also apply naturally to the arrival of the messages.