Learn Hardcore Icelandic: Ég hlusta á hljóðbók í strætó í stað þess að horfa á símann. - I listen to an audiobook on the bus instead of looking at the phone.

In Icelandic, the verb hlusta (to listen) almost always takes the preposition á with what you listen to: hlusta á e-ð.
So the standard pattern is:

hlusta á hljóðbók – listen to an audiobook
hlusta á tónlist – listen to music
hlusta á kennarann – listen to the teacher

Leaving out á (hlusta hljóðbók) is ungrammatical in normal Icelandic.

What case is hljóðbók in, and why?

Hljóðbók is in the accusative singular.
The verb–preposition combination hlusta á governs the accusative case for its object, so whatever you listen to will be in the accusative:

hlusta á hljóðbók (accusative)
hlusta á podcast (accusative)

If you made it definite, it would be hlusta á hljóðbókina (also accusative, with the definite ending).

Why is it í strætó and not á strætó?

Í means in, inside and is used when you are inside a vehicle or enclosed space. Á is more like on, on top of or onto.
Since you are physically inside the bus, Icelandic uses í strætó (in the bus), not á strætó (on the bus).
This is the same pattern as:

í bílnum – in the car
í lestinni – in the train

Which case is used in í strætó, and how can I tell?

With í you choose between accusative (movement into) and dative (location in).
Here it means on the bus / in the bus as a location, so í takes the dative. The noun strætó happens to look the same in nominative, accusative, and dative, but in this sentence it is grammatically dative.
Compare:

Ég fer í strætó – I go into / take the bus (accusative: motion into)
Ég er í strætó – I am on the bus (dative: location)

What does the phrase í stað þess að literally mean, and how is it built?

Literally, í stað þess að is in place of that to…

í stað – in place (stead)
þess – genitive of það (that), roughly of that
að – introduces the following verb in infinitive form

Together it is a fixed phrase meaning instead of (doing something), always followed by að + infinitive:

í stað þess að horfa á símann – instead of looking at the phone
í stað þess að sofa – instead of sleeping

Can I replace í stað þess að with something else, like in everyday speech?

Yes. A very common alternative is í staðinn fyrir (að):

Ég hlusta á hljóðbók í staðinn fyrir að horfa á símann.

You can also sometimes shorten it when the meaning is clear:

Ég hlusta á hljóðbók í staðinn. – I listen to an audiobook instead.

However, í stað þess að + infinitive is perfectly natural and common, also in everyday speech.

Why is it horfa á símann and not horfa símann or horfa í símann?

Like hlusta, the verb horfa (to look, to watch) normally takes á before its object: horfa á e-ð = look at / watch something.

horfa á símann – look at the phone
horfa á sjónvarpið – watch the TV
horfa á mynd – watch a movie

Horfa símann is ungrammatical. Horfa í símann exists, but it tends to mean more look into the phone (often with a nuance of staring into your phone), and it is less the neutral default than horfa á símann in a sentence like this.

Why does sími become símann here?

Sími is a masculine noun. In á símann, it is:

singular
accusative (because horfa á takes accusative)
definite (the phone, effectively my phone in context)

The definite article is attached as an ending: sími + inn → sím-inn.
In the accusative masculine singular, that ending surfaces as -ann, so we get símann.

Why is there no word for my before sími, like síminn minn?

Icelandic often uses the definite article alone to indicate something that is understood as the speaker’s own, especially very personal items in everyday contexts (phone, bed, car, keys, etc.).
So horfa á símann in a context like this is naturally understood as look at my phone, not look at the phone belonging to some random person.
You could say horfa á símann minn, but it would sound more explicit or contrastive (for example, if there are several phones and you want to stress which one).

Can I leave out Ég and just say Hlusta á hljóðbók í strætó…?

Normally, no. Icelandic is not a pronoun-dropping language like Spanish. The subject pronoun ég is usually required:
Ég hlusta á hljóðbók í strætó…

You only drop the subject in special situations (imperatives, headlines, notes/diaries where context is very clear, etc.), but in normal speech and writing you keep ég.

Is the word order fixed, or could I say Ég hlusta í strætó á hljóðbók?

The word order is somewhat flexible, but there is a preferred neutral order.

The most natural is:

Ég hlusta á hljóðbók í strætó í stað þess að horfa á símann.

You can say Ég hlusta í strætó á hljóðbók, but it sounds a bit marked or slightly less natural, unless you are emphasizing in the bus in contrast to some other place. In general, keep hlusta á [object] together, then add the location (í strætó) after it.

What is the difference between hlusta á and heyra?

hlusta á = listen to, active, intentional:
- Ég hlusta á hljóðbók. – I am listening to an audiobook.
heyra = hear, passive perception:
- Ég heyri hljóðbók. – I (can) hear an audiobook (it’s audible to me).

So in your sentence, since you are actively choosing to listen, hlusta á is the correct verb.

Is strætó an abbreviation or a slang word? Are there more formal alternatives?

Strætó is a shortened, colloquial form of strætisvagnur (literally street-vehicle, i.e. bus).
It is very common in everyday speech and not really considered slang anymore.
More formal or explicit options are:

í strætisvagni – in a bus
í strætisvagninum – in the bus (definite)

In everyday conversation, í strætó is what you will hear most.

What tense and person are hlusta and horfa here?

Both hlusta and horfa in this sentence are in the present indicative, first person singular:

Ég hlusta – I listen / I am listening
… í stað þess að horfa – instead of (for me) to look

The subject ég controls both verbs: I listen … instead of (I) looking at my phone. The second verb appears in the infinitive because of the í stað þess að construction.