Learn Hardcore Norwegian: Mange lyttere hører på radioen mens de lager middag. - Many listeners listen to the radio while they make dinner.

høre på radio – listen to the radio (the medium in general)
høre på radioen – often understood as listening to the radio device, or just “the radio” in a more concrete way

A lot of speakers use høre på radioen in a general sense too, so here it simply means “listen to the radio”, not necessarily a specific device you see in front of you.

Why is it Mange lyttere and not Mange lytterne?

Lyttere is the indefinite plural (listeners), and lytterne is the definite plural (the listeners).

Mange lyttere = many listeners (in general)
Mange av lytterne = many of the listeners (a specific group already known)

Since the sentence talks about listeners in general, not a specific group introduced earlier, the indefinite plural lyttere is correct.

How is the plural lyttere formed from lytter?

The noun lytter (listener) forms its regular plural like this:

Singular indefinite: en lytter – a listener
Singular definite: lytteren – the listener
Plural indefinite: lyttere – listeners
Plural definite: lytterne – the listeners

The pattern -er for plural indefinite and -ene (spelled -ne here) for plural definite is very common for masculine nouns in Bokmål.

Why is de used and not dem?

De is the subject pronoun (they), and dem is the object pronoun (them).

In mens de lager middag, the pronoun is the subject of the verb lager (they are the ones doing the action), so you must use de:

De lager middag. – They make dinner.
Vi ser dem. – We see them. (here dem is object)

Does de here clearly refer to lyttere?

Yes. De refers back to Mange lyttere.

So the structure is:

Mange lyttere (many listeners) … de (they)

This is just like English:

Many listeners listen to the radio while *they make dinner.*

Why is the verb in present tense (hører, lager) when in English we might say “are listening / are making”?

Norwegian normally uses the simple present for both:

English: They listen / They are listening
Norwegian: De hører

The same with lager:

English: They cook / They are cooking dinner
Norwegian: De lager middag

Norwegian does have a progressive form (er i ferd med å ..., driver og ...), but it is used much less often. The plain present tense covers both simple and continuous meanings in most cases.

What does mens do here, and what word order does it require?

Mens means while and introduces a subordinate clause (a dependent clause).

The clause is mens de lager middag:

mens – while
de – they (subject)
lager – make (verb)
middag – dinner (object)

In clauses introduced by mens, the normal word order is Subject – Verb – Object, just like here. So the word order is the same as in a main clause in this case.

Why is it lager middag and not something like er å lage middag?

Norwegian does not form the present progressive the same way English does. You normally do not say a literal equivalent of “are to make dinner”.

The natural Norwegian is simply:

De lager middag. – They are making / make dinner.

If you really want to emphasize that the action is in progress right now, you could say:

De holder på å lage middag. – They are in the middle of making dinner.

But for a general habit (what people commonly do), lager middag is exactly right.

Why is there no article before middag?

Meal names in Norwegian are usually used without an article when you talk about them in a general or habitual sense:

spise frokost – eat breakfast
lage middag – make dinner
ha lunsj – have lunch

You only use an article when you make it specific:

Middagen er klar. – The dinner is ready.
Jeg likte middagen vi hadde i går. – I liked the dinner we had yesterday.

Does middag always mean “dinner”? Could it also mean “lunch”?

Traditionally in Norway, middag is the main hot meal of the day, which was often eaten in the afternoon (closer to “lunch” time). Today many people eat middag later, in the evening, so it often corresponds to English dinner or supper.

The key idea is “the main cooked meal”, not the exact clock time.

What is the difference between høre and lytte?

høre = to hear
høre på = to listen (to)
lytte (til) = to listen (to), often with a nuance of listening carefully, attentively

In practice:

høre på radioen – listen to the radio (normal, everyday expression)
lytte til radioen – also possible, sounds a bit more formal or focused on the act of attentive listening.

In this sentence, hører på radioen is the most idiomatic choice.