I radioen hører vi en nyhed om vejret, mens vi laver morgenmad.

Because Danish often puts a time/place/context expression first to set the scene. Here, I radioen tells you where the news is being heard: on the radio.

When a sentence starts with something other than the subject, Danish usually uses inversion, so the verb comes before the subject:

• I radioen hører vi ...
• not I radioen vi hører ...

This is a very common Danish pattern.

This is the normal Danish V2 word order rule. In main clauses, the finite verb usually comes in the second position.

So if the sentence begins with the subject, you get:

• Vi hører en nyhed ...

But if something else comes first, such as I radioen, then the verb still has to stay in second position:

• I radioen hører vi en nyhed ...

So hører vi is not unusual here; it is exactly what Danish grammar requires.

This is just one of those preposition differences between Danish and English.

Danish commonly says:

• i radioen = on the radio
• i fjernsynet = on TV

So even though i often means in, you should learn i radioen here as the natural Danish expression.

Radioen means the radio.

It comes from:

• en radio = a radio
• radioen = the radio

Danish usually adds the definite article to the end of the noun instead of putting a separate word in front, unlike English.

So:

• en radio = a radio
• radioen = the radio

In English, news is usually uncountable, but Danish nyhed is a countable noun.

So:

• en nyhed = a news item / a piece of news
• nyheder = news items
• nyhederne = the news

That means en nyhed om vejret is very natural Danish, even though in English you would probably say a weather report or a piece of news about the weather rather than a news.

Yes, depending on context, that can be a more natural English translation.

Literally, en nyhed om vejret is a news item about the weather, but in natural English, a weather report may sound better.

Still, the Danish wording is fine. It simply focuses on a piece of news concerning the weather.

Because Danish normally uses the definite form vejret when talking about the weather in a general sense.

So:

• vejr = weather / a type of weather
• vejret = the weather

That is why om vejret means about the weather.

It comes from the neuter noun:

• et vejr = a weather / weather
• vejret = the weather

For many neuter nouns, the definite form adds -et:

• et hus → huset
• et vejr → vejret

So om vejret is simply about the weather.

Mens means while.

It connects two actions that happen at the same time:

• I radioen hører vi en nyhed om vejret
• mens vi laver morgenmad

So the meaning is that the hearing and the breakfast-making are happening simultaneously.

Because mens introduces a subordinate clause.

In Danish subordinate clauses, the word order is usually more like English:

• mens vi laver morgenmad

Here the subject vi comes before the verb laver.

Compare:

• main clause: I radioen hører vi ...
• subordinate clause: mens vi laver morgenmad

So this sentence is useful because it shows both main-clause word order and subordinate-clause word order.

Danish does not have a separate tense form like the English present progressive.

So Danish often uses the simple present where English uses either:

• we hear
• we are hearing
• we make
• we are making

In this sentence:

• hører can correspond to hear or are hearing
• laver can correspond to make or are making

The context tells you that these actions are happening now or as part of a routine.

Because laver morgenmad means make breakfast or prepare breakfast, not eat breakfast.

So the sentence says that while we are preparing breakfast, we hear a weather news item on the radio.

If you wanted while we eat breakfast, you would say:

• mens vi spiser morgenmad

Meal words in Danish often appear without an article when speaking generally.

So Danish says:

• spise morgenmad = eat breakfast
• lave morgenmad = make breakfast

This is similar to English, where we usually say eat breakfast, not eat a breakfast, unless we mean one specific breakfast in a special sense.

Laver is the present tense of lave, which often means make, do, or prepare.

In this sentence, it means prepare or make:

• vi laver morgenmad = we are making breakfast

It is a very common everyday verb in Danish.

Yes. That version is also grammatical.

The difference is mostly one of emphasis:

• I radioen hører vi ... puts the focus first on on the radio
• Vi hører ... i radioen starts more neutrally with we

Both are fine, but the original sentence highlights the setting first.

Because mens vi laver morgenmad is a subordinate clause, and many Danish writers place a comma before such clauses.

So the comma helps separate:

• the main clause: I radioen hører vi en nyhed om vejret
• the subordinate clause: mens vi laver morgenmad

You may also notice some variation in Danish comma use depending on style and comma system, but the comma here is completely normal.