Hún notar heyrnartól á bókasafninu, því hátalarinn á símanum væri of hávær þar.

Here því means because / since and introduces the reason.

So the structure is:

• Hún notar heyrnartól ...
• því ...

A very common everyday alternative is af því að for because. The bare því can sound a bit shorter or more written/formal.

Do not confuse this with other uses of því, such as the pronoun form meaning things like therefore, by that, or for that reason in other contexts.

Væri is the past subjunctive of vera (to be), and here it gives a hypothetical meaning: would be.

So the idea is not just:

• the phone speaker is too loud there

but rather:

• the phone speaker would be too loud there

That fits the logic of the sentence: she uses headphones because using the phone’s speaker in that setting would be too loud.

If the speaker wanted to present it as a plain fact, they would more likely use er:

• ... því hátalarinn á símanum er of hávær þar.

Not really.

Even though væri is historically a past subjunctive form, in sentences like this it often expresses unreal / hypothetical / conditional meaning rather than past time. So here it is best understood as would be, not was.

That is very common in Icelandic:

• er = is
• var = was
• væri = would be / were

No. Icelandic of here means too or excessively.

So:

• of hávær = too loud

It has nothing to do with the English preposition of.

A very common beginner mistake is to read Icelandic of as if it were English of, but they are unrelated in meaning here.

Because Icelandic often uses á with certain places and institutions where English might say in or at.

So:

• á bókasafninu = at/in the library

This is largely something you learn as part of the noun’s normal usage. Prepositions in Icelandic do not always line up neatly with English ones.

They are in the dative, because á takes the dative when it expresses a static location.

Here both phrases describe location or position, not movement:

• á bókasafninu = at the library
• á símanum = on the phone

So you get dative forms:

• bókasafnið → bókasafninu
• síminn → símanum

A useful rule of thumb is:

• á + dative = location
• á + accusative = motion toward / onto

Þar means there, and it points back to the library.

It avoids repeating the full place phrase again:

• á bókasafninu ... þar
  = at the library ... there

It also slightly reinforces the idea that in that place, using the speaker would be too loud.

In some contexts it could be left out, but keeping it sounds natural and clear.

Heyrnartól is the direct object of notar, and nota takes the accusative.

So in grammatical terms, heyrnartól is accusative here.

The reason you do not see an obvious special ending is that this word has the same surface form in the relevant pattern here. That is very common with many neuter nouns in Icelandic.

So the important point for a learner is:

• nota
  • accusative
• heyrnartól is the thing being used

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

For example:

• hátalari = a speaker

• hátalarinn = the speaker

• sími = a phone

• símanum = the phone (dative)

• bókasafn = a library
• bókasafninu = the library (dative)

So where English says the library, Icelandic often says one word: bókasafnið or, in another case form, bókasafninu.

It means the speaker on the phone or the phone’s speaker.

So á símanum belongs with hátalarinn and tells you which speaker is being talked about.

This is important for understanding the sentence correctly: it is not talking about some separate loudspeaker nearby, but specifically the speaker built into the phone.

Because á símanum is part of the noun phrase hátalarinn á símanum.

In other words, the subject is not just hátalarinn by itself, but:

• hátalarinn á símanum = the speaker on the phone

So the clause is structured like this:

• [hátalarinn á símanum] [væri] [of hávær] [þar]

That is normal Icelandic word order. The descriptive phrase stays with the noun it belongs to before the verb.

Yes. Icelandic loves compounds, and heyrnartól is one of them.

It is made from:

• heyrn = hearing
• tól = tool, device, equipment

So the literal sense is something like hearing device/equipment, which becomes headphones / headset in normal English.

This is a very typical Icelandic way of building vocabulary: smaller native words combine into a longer, precise compound.