Farþegarnir bíða rólega á meðan bílstjórinn talar við lögregluna.

They are both forms of the suffixed definite article in Icelandic.

Unlike English, which usually puts the before a noun, Icelandic often attaches the definite article to the end of the noun:

• farþegar = passengers

• farþegarnir = the passengers

• bílstjóri = driver
• bílstjórinn = the driver

So Icelandic often says the equivalent of passengers-the and driver-the.

The exact shape of the ending changes depending on:

• gender
• number
• case

That is why one noun ends in -nir and the other in -inn.

Because the sentence is talking about:

• the passengers as a group
• the driver as one person

So:

• farþegarnir = nominative plural definite, from farþegi = passenger
• bílstjórinn = nominative singular definite, from bílstjóri = driver

This matches the verbs too:

• Farþegarnir bíða = the passengers wait / are waiting
• bílstjórinn talar = the driver speaks / is speaking

Because in the present tense, Icelandic verbs do not always have a separate plural form that looks different from the infinitive.

Here:

• að bíða = to wait
• ég bíð = I wait
• þú bíður = you wait
• hann/hún/það bíður = he/she/it waits
• við bíðum = we wait
• þið bíðið = you all wait
• þeir/þær/þau bíða = they wait

So farþegarnir bíða is simply the normal they form.

By contrast:

• að tala = to speak
• hann talar = he speaks

That is why the second verb is talar, because the subject there is singular: bílstjórinn.

Rólega is an adverb, meaning something like calmly or quietly.

It comes from the adjective rólegur = calm, quiet.

A very common pattern in Icelandic is:

• adjective + -a → adverb

For example:

• hraður = fast
• hratt = quickly
• rólegur = calm
• rólega = calmly

So Farþegarnir bíða rólega means the passengers are waiting calmly.

Á meðan means while.

It introduces a clause describing something happening at the same time as the main action:

• Farþegarnir bíða rólega = the passengers are waiting calmly
• á meðan bílstjórinn talar við lögregluna = while the driver is talking to the police

So the whole sentence has:

• a main clause
• a time clause introduced by á meðan

This is a very common way to connect simultaneous actions.

Because the verb tala við means talk to or speak with, and the preposition við takes the accusative case here.

The base form is:

• lögregla = police

But after við, it becomes:

• lögregluna = the police (accusative singular definite)

So:

• tala við einhvern = talk to someone
• tala við lögregluna = talk to the police

This is one of those combinations that you usually learn together:

• tala við = speak/talk with
• bíða eftir = wait for
  and so on

In this sentence, bíða is used without an object, so it just means wait.

In Icelandic, lögreglan is often treated as a singular collective noun, even when English uses the plural-looking expression the police.

So:

• lögregla = police
• lögreglan = the police

Even though it refers to the police as an institution or authority, the grammar is singular.

That is why you get:

• við lögregluna = with / to the police

This is normal Icelandic usage.

The basic order is very similar to English:

• Farþegarnir = subject
• bíða = verb
• rólega = adverb
• á meðan ... = subordinate time clause

Then inside the second clause:

• bílstjórinn = subject
• talar = verb
• við lögregluna = prepositional phrase

So the structure is:

[The passengers] [wait] [calmly] [while [the driver] [talks] [to the police]].

Nothing especially unusual is happening here. It is a good example of straightforward Icelandic sentence order.

Yes.

Icelandic present tense often covers both:

• a general present: wait
• an ongoing present: are waiting

So:

• Farþegarnir bíða rólega can mean the passengers wait calmly
• but in normal context it will usually be understood as the passengers are waiting calmly

Likewise:

• bílstjórinn talar við lögregluna can mean the driver talks to the police
• or the driver is talking to the police

Context tells you which one is meant.

Yes, several.

A few important ones:

• þ in Farþegarnir is like the th in thin
• ð in bíða is like the th in this (though in Icelandic it can be softer depending on position)
• í is a long ee sound
• á is not like English short a; it is more like an ow/au-type vowel
• ll in talar is just a normal l sound here
• regl in lögregluna can feel consonant-heavy for English speakers, so it helps to say it slowly at first

A rough beginner-friendly pronunciation guide might be:

• Farþegarnir ≈ FAR-theh-gar-nir
• bíða ≈ BEE-tha
• rólega ≈ RO-leh-ga
• á meðan ≈ ow MEH-than
• bílstjórinn ≈ BEEL-styour-inn
• talar ≈ TAH-lar
• við lögregluna ≈ vith LUR-reh-klu-na

That is only approximate, but it can help you get started.

In this sentence:

• farþegarnir is nominative plural
• bílstjórinn is nominative singular
• lögregluna is accusative singular

Why?

Because:

• farþegarnir is the subject of bíða
• bílstjórinn is the subject of talar
• lögregluna comes after við, which requires the accusative here

So this sentence is a nice small example of how Icelandic case works:

• subjects are in the nominative
• some prepositions, such as við in this usage, require the accusative