Patienten spørger, om undersøgelsen tager lang tid, fordi hun skal tilbage på arbejde.

Patienten means the patient, while en patient means a patient.

In Danish, the definite article is often added to the end of the noun:

• en patient = a patient
• patienten = the patient

So Patienten spørger ... means The patient asks ...

Spørger is the present tense of at spørge = to ask.

• at spørge = to ask
• spørger = asks / is asking
• spurgte = asked
• spørg! = ask! (imperative)

So Patienten spørger means The patient asks or The patient is asking, depending on context.

Here, om means whether / if.

In this sentence:

• Patienten spørger, om undersøgelsen tager lang tid
  = The patient asks whether the examination takes a long time

This is very common in Danish after verbs like spørge when introducing an indirect yes/no question.

Compare:

• Hun spørger, om det gør ondt. = She asks if it hurts.
• Jeg ved ikke, om han kommer. = I don’t know whether he is coming.

So this om is not the same as the om that can mean about or in/about time in other contexts.

Because this is a subordinate clause, introduced by om.

In Danish main clauses, the finite verb usually comes in second position:

• Undersøgelsen tager lang tid.
  = The examination takes a long time.

But in subordinate clauses, Danish usually has a more straightforward subject-verb order:

• ... om undersøgelsen tager lang tid
  = ... whether the examination takes a long time

So after om, you normally do subject + verb:

• om hun kommer
• om det er rigtigt
• om undersøgelsen tager lang tid

Undersøgelsen means the examination or the test/check-up, depending on context.

It comes from:

• en undersøgelse = an examination / an investigation / a test
• undersøgelsen = the examination

Again, the definite ending is attached to the noun:

• -en is the definite ending for many common gender nouns

So:

• en undersøgelse
• undersøgelsen

Yes. At tage often means to take, and in the expression tage lang tid, it works just like English take a long time.

• Undersøgelsen tager lang tid. = The examination takes a long time.
• Det tager fem minutter. = It takes five minutes.

This is a very common expression in Danish.

A few related examples:

• Det tager ikke lang tid. = It doesn’t take long.
• Hvor lang tid tager det? = How long does it take?

Because the subject is already undersøgelsen.

In English, we might sometimes say The examination takes a long time, and that is exactly what Danish is doing here. There is no need for a separate it.

Compare:

• Undersøgelsen tager lang tid. = The examination takes a long time.
• Det tager lang tid. = It takes a long time.

Both are possible, but they mean slightly different things structurally:

• undersøgelsen = the examination is the subject
• det = it is the subject

Fordi means because.

It introduces the reason:

• Patienten spørger ... fordi hun skal tilbage på arbejde.
• The patient asks ... because she has to go back to work.

Like om, fordi introduces a subordinate clause.

No, this is natural gender, not grammatical gender.

Hun means she, referring to the patient as a female person. If the patient were male, it would be han.

• fordi hun skal tilbage på arbejde = because she has to go back to work
• fordi han skal tilbage på arbejde = because he has to go back to work

This has nothing to do with the grammatical gender of patient or undersøgelse.

Here skal is best understood as has to or needs to.

• hun skal tilbage på arbejde
  = she has to go back to work

Danish skal can cover meanings like shall, must, or be supposed to, depending on context. In this sentence, the natural English meaning is has to.

Some examples:

• Jeg skal hjem nu. = I have to go home now.
• Du skal ringe til lægen. = You must / should call the doctor.
• Vi skal mødes klokken otte. = We are supposed to meet at eight.

Tilbage means back.

So:

• tilbage på arbejde = back to work

Examples:

• Jeg skal tilbage til kontoret. = I have to go back to the office.
• Hun kom tilbage i går. = She came back yesterday.

In your sentence, skal tilbage på arbejde means the patient needs to return to work.

Both på arbejde and til arbejde exist, but they are used differently.

• på arbejde often describes being at work / in a work situation
• til arbejde often emphasizes movement toward work

In tilbage på arbejde, Danish commonly uses på arbejde to express returning to the state or place of being at work:

• Hun skal tilbage på arbejde. = She has to go back to work.

This is a fixed and very common expression.

Compare:

• Jeg er på arbejde. = I am at work.
• Jeg går på arbejde. = I go to work.
• Jeg tager til arbejde nu. = I’m heading to work now.
  This is possible in some contexts, but på arbejde is often the more idiomatic phrase in general expressions.

Because Danish punctuation normally places commas before subordinate clauses.

Here you have:

• Patienten spørger, om undersøgelsen tager lang tid, fordi hun skal tilbage på arbejde.

The clause starting with om is subordinate, so a comma comes before it.
The clause starting with fordi is also subordinate, so it is separated with a comma as well.

Danish comma rules can feel more systematic than English ones in this area, especially in formal writing.

In normal reading, it refers to the reason the patient is asking.

So the meaning is:

• The patient asks whether the examination will take a long time, because she has to go back to work.

In other words, her need to return to work explains why she is asking.

Grammatically, learners sometimes wonder whether it could attach to tager lang tid, but context strongly favors the first interpretation.

Yes, this sentence is perfectly natural, especially in written or semi-formal spoken Danish.

In everyday speech, people might also say things like:

• Patienten spørger, om undersøgelsen kommer til at tage lang tid, fordi hun skal tilbage på arbejde.
• Hun spørger, om det tager lang tid, fordi hun skal tilbage på arbejde.

These are slightly different in style:

• tager lang tid = takes a long time
• kommer til at tage lang tid = is going to take a long time

Your original sentence is clear, correct, and very standard.