Hvis jeg arbejder sjusket, laver jeg let fejl.

Hvis means if. It introduces a condition:

• Hvis jeg arbejder sjusket = If I work sloppily / If I work carelessly

It is used for real or general conditions, just like English if.

Because hvis jeg arbejder sjusket is a subordinate clause. In Danish subordinate clauses, the subject normally comes before the verb:

• hvis jeg arbejder
• fordi jeg arbejder
• når jeg arbejder

So jeg arbejder is the normal order here.

This is because the sentence starts with the if-clause:

• Hvis jeg arbejder sjusket, ...

When a non-subject element comes first in a Danish main clause, the verb usually comes before the subject. This is the normal V2 word order in Danish:

• Hvis jeg arbejder sjusket, laver jeg let fejl.

If you put the main clause first, you get normal subject-verb order there:

• Jeg laver let fejl, hvis jeg arbejder sjusket.

Both are correct.

Sjusket means sloppy, careless, or messy in the way you work.

In this sentence it functions adverbially: it describes how you work:

• arbejder sjusket = work sloppily / carelessly

Danish often uses the same form for an adjective and for an adverb-like meaning, especially in cases like this.

Compare:

• et sjusket arbejde = a sloppy piece of work
• han arbejder sjusket = he works sloppily

Yes, let can mean light, but here it means easily.

This is the adverbial use of let:

• jeg laver let fejl = I easily make mistakes

So in this sentence, let is not about weight. It means something like:

• easily
• readily

Sometimes, but not always with exactly the same feel.

• let often means easily / readily
• nemt often means easily in the sense of without difficulty

In this sentence, let sounds very natural:

• Jeg laver let fejl = I easily make mistakes

Jeg laver nemt fejl is possible, but let is especially idiomatic here.

Yes, and that is perfectly normal Danish. At lave fejl is a very common expression meaning to make mistakes.

Examples:

• Hun laver tit fejl. = She often makes mistakes.
• Jeg lavede en fejl. = I made a mistake.

You may also see begå fejl, but lave fejl is more everyday and common.

Because fejl has the same form in singular and plural in many uses.

So:

• en fejl = a mistake
• flere fejl = several mistakes

In the phrase lave fejl, Danish often uses the bare plural-like form without an article:

• laver fejl = make mistakes

That is completely normal.

It is in the present tense:

• arbejder = work / am working
• laver = make / am making

Here the present tense expresses a general truth or a habitual result:

• If I work carelessly, I make mistakes easily.

It is not just about one specific moment; it can describe what generally happens.

Mostly a general rule.

Hvis jeg arbejder sjusket, laver jeg let fejl means something like:

• Whenever I work carelessly, I easily make mistakes
• If I work carelessly, I tend to make mistakes

Danish often uses the present tense for this kind of general cause-and-effect statement.

Yes. In normal Danish writing, the subordinate clause is separated from the main clause with a comma:

• Hvis jeg arbejder sjusket, laver jeg let fejl.

So the comma here is correct and expected.

Yes:

• Jeg laver let fejl, hvis jeg arbejder sjusket.

This means the same thing. The difference is mainly one of emphasis and word order.

With the if-clause first, the condition is foregrounded:

• Hvis jeg arbejder sjusket, laver jeg let fejl.

With the main clause first, the result is stated first:

• Jeg laver let fejl, hvis jeg arbejder sjusket.

It often suggests something a bit more like sloppy, untidy, or done without enough care.

So arbejde sjusket is not just being accidentally careless once; it can imply a messy, slapdash way of working.

Possible English shades of meaning are:

• carelessly
• sloppily
• in a slapdash way

Which one fits best depends on context.