Hans arbejde er sjusket, når han har travlt.

Here it most naturally means work in the sense of the work he produces or what he is doing.

Because the sentence says it is sjusket (sloppy/careless), it is talking about the quality of his work, not really his occupation. So this could describe his schoolwork, writing, repairs, office work, and so on.

Because sit/sin/sine is a reflexive possessive that refers back to the subject of the clause.

In Hans arbejde er sjusket, the grammatical subject is arbejde, not han. So Danish uses hans, not sit.

A useful comparison:

• Han elsker sit arbejde. = He loves his own work/job.
  Here the subject is han, so sit can refer back to him.

• Hans arbejde er sjusket. = His work is sloppy.
  Here the subject is arbejde, so you use hans.

Yes. Arbejde can be both:

• a noun: work
• a verb: to work

In this sentence, it is clearly a noun, because it comes after the possessive Hans and acts as the subject of the sentence: Hans arbejde = his work.

Sjusket means something like:

• sloppy
• careless
• messy
• poorly done

It usually describes work or behavior that lacks care or attention to detail.

So Hans arbejde er sjusket suggests that the result of his work is not neat, accurate, or careful.

Sjusket is the normal adjective form you use here. It already ends in -et as part of the word.

You can think of it like this:

• en sjusket elev = a sloppy student
• et sjusket arbejde = sloppy work
• arbejdet er sjusket = the work is sloppy

So in this sentence, sjusket is just the correct adjective form to describe arbejde.

Har travlt is a very common Danish expression meaning:

• is busy
• is in a rush
• has a lot to do

So når han har travlt means when/whenever he is busy.

In this sentence, busy is probably the best translation.

Because have travlt is a fixed Danish expression.

You normally say:

• Jeg har travlt.
• Han har travlt.
• Vi har travlt.

You do not normally say har travl.

By contrast, travl can appear before a noun:

• en travl dag = a busy day
• en travl mand = a busy man

So:

• travl is common before nouns
• travlt is what you use in the expression have travlt

Because når han har travlt is a subordinate clause, and Danish normally puts a comma before subordinate clauses.

So the structure is:

• Hans arbejde er sjusket = main clause
• når han har travlt = subordinate clause

That is why the comma is there.

Når means when or whenever, while hvis means if.

In this sentence, the idea is that whenever he is busy, his work becomes sloppy. That is a repeated or typical situation, so når is the natural choice.

Compare:

• Når han har travlt, er hans arbejde sjusket.
  = When/whenever he is busy, his work is sloppy.

• Hvis han har travlt, bliver hans arbejde sjusket.
  = If he is busy, his work becomes sloppy.

The second version sounds more conditional or hypothetical.

Because når han har travlt is a subordinate clause, and subordinate clauses in Danish usually keep the normal order:

• subject + verb

So:

• han har travlt

In main clauses, Danish often uses verb-second word order, but subordinate clauses do not follow that same pattern in the same way.

Compare:

• Han har travlt. = main clause
• når han har travlt = subordinate clause

You would not say når har han travlt here.

It can mean either, depending on how natural the English sounds.

In this sentence, whenever is often the best explanation, because it describes a general pattern:

• His work is sloppy whenever he is busy.

But in smoother English, people may simply say:

• His work is sloppy when he is busy.

So for a learner, it is useful to understand når here as expressing a regular situation, not just one single moment.

Yes. Danish can also say:

• Når han har travlt, er hans arbejde sjusket.

That means the same thing.

The main difference is emphasis:

• Hans arbejde er sjusket, når han har travlt.
  starts with the main point: his work is sloppy

• Når han har travlt, er hans arbejde sjusket.
  starts with the condition: when he is busy

If the subordinate clause comes first, the main clause shows inversion:

• Når han har travlt, er hans arbejde sjusket.

Notice er comes before hans arbejde in the second clause.