I dag steger min mand kyllingen, mens jeg skærer brød.

This is because Danish main clauses follow the V2 rule: the finite verb must come in the second position.

Here, I dag is placed first for emphasis, so the verb steger has to come next:

• I dag steger min mand kyllingen ...

If the subject comes first, then the order is more like English:

• Min mand steger kyllingen i dag.

So Danish is not simply moving words around freely. When something other than the subject is put first, the verb still stays in second place.

Yes. I dag means today, and it can often appear in different positions depending on emphasis.

For example:

• I dag steger min mand kyllingen, mens jeg skærer brød.
• Min mand steger kyllingen i dag, mens jeg skærer brød.

Both are natural, but they feel slightly different:

• putting I dag first highlights today
• putting it later is often more neutral

So the version in your sentence gives today a bit of focus.

In Danish, the ordinary present tense often covers both:

• simple present: fries / cuts
• present progressive: is frying / am cutting

So:

• min mand steger kyllingen can mean my husband fries the chicken or my husband is frying the chicken
• jeg skærer brød can mean I cut bread or I am cutting bread

Context usually makes it clear. Here, with i dag and mens, it naturally sounds like something happening now.

If Danish wants to stress that something is in progress, it can use other expressions, such as:

• er ved at ... = is in the middle of ...

For example:

• Min mand er ved at stege kyllingen.

But the plain present tense is very common.

They are present-tense forms of the verbs:

• at stege = to fry / roast
• at skære = to cut

In Danish, the present tense is usually made by adding -r to the infinitive:

• stege → steger
• skære → skærer

A useful thing for English speakers: Danish verbs do not change for person.

So you get:

• jeg steger
• du steger
• han steger
• vi steger

The verb form stays the same.

Danish usually puts the definite article at the end of the noun instead of using a separate word like English the.

So:

• en kylling = a chicken
• kyllingen = the chicken

The ending -en is the definite ending for many common-gender nouns.

This is one of the biggest structural differences from English. Instead of:

• the + noun

Danish often uses:

• noun + definite ending

So kyllingen literally works like chicken-the, even though in natural English we say the chicken.

Because brød here is being used as a mass noun, like bread in English.

So:

• jeg skærer brød = I am cutting bread

This means bread in a general, non-specific sense, not the bread.

Compare:

• jeg skærer brød = I am cutting bread
• jeg skærer brødet = I am cutting the bread
• jeg skærer et brød = I am cutting a loaf / a bread (depending on context, often a loaf)

So the sentence is using the more general, natural mass-noun form.

Mens means while.

It introduces a subordinate clause:

• mens jeg skærer brød

In Danish, subordinate clauses do not follow the same V2 pattern as main clauses. So after mens, the subject normally comes before the verb:

• mens jeg skærer brød

not

• mens skærer jeg brød

This is an important contrast:

• main clause: V2 word order
  
  • I dag steger min mand kyllingen
• subordinate clause: more straightforward subject + verb order
  
  • mens jeg skærer brød

Because mens jeg skærer brød is a subordinate clause, and many Danish writers put a comma before such clauses.

So:

• I dag steger min mand kyllingen, mens jeg skærer brød.

This is a normal and correct way to write it.

You may also see variation depending on comma style, but for a learner, it is very useful to notice that mens often introduces a clause that gets separated with a comma in writing.

In ordinary Danish, min mand usually means my husband.

Word-for-word, it looks like my man, but that is not usually how it is understood in everyday Danish.

So:

• mand can mean man
• but min mand usually means my husband

If someone means my boyfriend / partner, they would more often say something like:

• min kæreste

So in this sentence, min mand is most naturally understood as my husband.

These are Danish vowels that do not match English exactly.

In your sentence:

• skærer contains æ
• brød contains ø
• kyllingen contains y

A rough guide:

• æ is somewhat like the vowel in cat, though not exactly the same
• ø has no exact English equivalent; it is similar to German ö or French eu
• y also has no exact English equivalent; it is similar to German ü or French u

So these words can be tricky for English speakers:

• skærer
• brød
• kyllingen

It is best to learn them by listening and repeating, because English spelling habits will not help much here.

It is singular.

• kylling = chicken
• kyllingen = the chicken

So the sentence is talking about one specific chicken.

The plural forms would be different:

• kyllinger = chickens
• kyllingerne = the chickens

Here, the singular makes sense because it is probably referring to one chicken being cooked.