Min bror arbejder sjusket, når han har travlt, men min søster er grundig hele tiden.

Because bror and søster are common-gender nouns in Danish, so the possessive is min:

• min bror = my brother
• min søster = my sister

You use:

• min with common-gender singular nouns
• mit with neuter singular nouns
• mine with plural nouns

For example:

• min bil = my car
• mit hus = my house
• mine bøger = my books

In this sentence, sjusket functions like an adverb meaning sloppily/carelessly.

Many Danish adjectives can be used adverbially, often in the neuter form. With sjusket, the form already looks like -et, so it stays sjusket:

• Han er sjusket. = He is sloppy.
• Han arbejder sjusket. = He works sloppily.

So even though it describes how he works, the form is still sjusket.

It is originally an adjective, but here it is being used adverbially to describe the way he works.

So:

• en sjusket person = a sloppy person
• arbejde sjusket = to work sloppily

English often adds -ly to make adverbs, but Danish usually does not do that in the same way. Instead, an adjective form is often used adverbially.

Når means when in the sense of something that happens repeatedly or generally.

So here:

• når han har travlt = when he is busy / when he’s in a hurry

This suggests a repeated pattern: whenever he is busy, he works sloppily.

A useful contrast:

• når = when, whenever, in general
• da = when, at a specific time in the past

Examples:

• Når jeg er træt, drikker jeg kaffe. = When I am tired, I drink coffee.
• Da jeg var barn, boede jeg i Aarhus. = When I was a child, I lived in Aarhus.

Have travlt is a very common Danish expression meaning to be busy or to be in a rush.

So Danish usually says:

• Jeg har travlt. = I’m busy.
• Han har travlt. = He’s busy.

You may also see travl as a normal adjective in other contexts, but in everyday Danish, have travlt is the standard expression for being busy.

In the expression have travlt, Danish uses the neuter form travlt. This is part of the fixed idiomatic expression.

So you learn it as a chunk:

• at have travlt = to be busy

Even though travl is the dictionary form, the usual phrase is have travlt, not have travl.

Because når introduces a subordinate clause, and subordinate clauses in Danish normally keep the order subject + verb:

• når han har travlt

So:

• han = subject
• har = verb

This is different from main clauses, where Danish often has verb-second word order.

Compare:

• Han arbejder sjusket, når han har travlt.
• Når han har travlt, arbejder han sjusket.

In both cases, inside the når clause, it stays han har.

Men means but and connects two contrasting ideas:

• Min bror arbejder sjusket, når han har travlt
• men min søster er grundig hele tiden

The contrast is:

• brother: sloppy when busy
• sister: thorough all the time

So men sets up that opposition.

Both are possible in Danish, but they mean slightly different things.

• er grundig = is thorough (describes her general quality or character)
• arbejder grundigt = works thoroughly (describes the way she works in that situation)

In this sentence, min søster er grundig hele tiden emphasizes that thoroughness is a constant trait of the sister, not just the way she happens to work once.

Because here grundig is a predicate adjective after er, describing min søster.

Since søster is a common-gender singular noun, the adjective stays in the common singular form:

• min søster er grundig

Compare:

• en grundig søster
• min søster er grundig
• et grundigt arbejde = a thorough piece of work
• hun arbejder grundigt = she works thoroughly

So grundigt would be used with a neuter noun or adverbially, not here after er with søster.

Hele tiden means all the time or constantly.

In this sentence, it means the sister is thorough all the time, not only under certain conditions.

Examples:

• Han klager hele tiden. = He complains all the time.
• Hun tænker på arbejde hele tiden. = She thinks about work all the time.

Yes. You could say:

• Når han har travlt, arbejder min bror sjusket, men min søster er grundig hele tiden.

That is also correct.

If a subordinate clause comes first in Danish, the main clause usually has inversion, so the verb comes before the subject:

• Når han har travlt, arbejder min bror sjusket.

Not:

• Når han har travlt, min bror arbejder sjusket.

The commas mark clause boundaries.

• The comma before når separates the main clause from the subordinate clause.
• The comma before men separates two coordinated clauses.

So the structure is easier to see:

• Min bror arbejder sjusket, når han har travlt,
• men min søster er grundig hele tiden.

Modern Danish punctuation regularly uses commas like this.

Yes. In this sentence, han clearly refers to min bror.

So the first part means:

• My brother works sloppily when he is busy

Then the sentence switches to:

• but my sister is thorough all the time

This kind of pronoun reference is very normal and natural in Danish.

A rough guide for an English speaker is:

• Min bror ≈ meen brohr
• arbejder ≈ AR-bye-der
• sjusket ≈ SHOOS-ked
• når ≈ nor
• han har travlt ≈ han har trowlt
• men min søster ≈ men meen SUR-ster
• er grundig ≈ air GRUN-dee
• hele tiden ≈ HAY-leh TEE-dən

But Danish pronunciation is often much softer and less clearly pronounced than spelling suggests, so it is best to treat this only as a rough starting point.