Hennes skjorta är fortfarande skrynklig, så hon vill stryka den innan hon går till jobbet.

Because sin/sitt/sina is a reflexive possessive, and it refers back to the subject of the clause.

In Hennes skjorta är fortfarande skrynklig, the subject is skjorta, not hon. So Swedish uses hennes.

Compare:

• Hon stryker sin skjorta. = She irons her own shirt.
  
  • Here the subject is hon, so sin works.
• Hennes skjorta är skrynklig. = Her shirt is wrinkled.
  
  • Here the subject is skjorta, so sin would not fit.

Because the adjective must agree with the noun it describes.

Skjorta is:

• a common gender noun (en skjorta)
• singular
• indefinite

So the adjective form is skrynklig.

Compare:

• en skrynklig skjorta = a wrinkled shirt
• ett skrynkligt plagg = a wrinkled garment
• skrynkliga skjortor = wrinkled shirts

The same agreement appears after är as well:

• Skjortan är skrynklig.

Here fortfarande means still.

So är fortfarande skrynklig = is still wrinkled.

In many cases, fortfarande and ännu can both translate as still, but fortfarande is often the more neutral and common choice for ongoing situations.

Examples:

• Hon sover fortfarande. = She is still sleeping.
• Hon sover ännu. = She is still sleeping.
  
  • This can sound a bit more formal or literary in some contexts.

So in this sentence, fortfarande is very natural.

Because stryka is a transitive verb here: you iron something.

The object is the shirt, and Swedish normally keeps that object explicit:

• hon vill stryka den = she wants to iron it

Using den avoids repeating skjortan/skjorta.

You could also say:

• ...så hon vill stryka skjortan innan hon går till jobbet.

That is also correct, but den sounds more natural when the shirt has just been mentioned.

Because skjorta is an en-word.

In Swedish:

• en-words are referred to by den
• ett-words are referred to by det

Since it is:

• en skjorta

the correct pronoun is:

• den

Example:

• Jag köpte en skjorta. Den är dyr.
• Jag köpte ett plagg. Det är dyrt.

Swedish often uses the present tense to talk about future events when the time is understood from the context.

So:

• innan hon går till jobbet literally looks like before she goes to work
• but naturally means before she goes to work / before she leaves for work

This is very common in Swedish.

Compare:

• Jag ringer dig när jag kommer hem. = I’ll call you when I get home.
• Vi äter innan vi går. = We’ll eat before we leave.

You could say innan hon ska gå till jobbet, but that slightly changes the nuance and is not as simple or natural here.

Swedish normally requires an explicit subject in a clause.

So Swedish says:

• innan hon går till jobbet

English can often shorten this to:

• before going to work

But Swedish usually does not do that in the same easy way. The full clause with hon is the normal choice.

Because till shows movement toward a destination.

• gå till jobbet = go to work
• vara på jobbet = be at work

So:

• innan hon går till jobbet = before she goes to work
• hon är på jobbet = she is at work

This is the same idea as:

• åka till skolan = go to school
• vara i skolan / på skolan = be in/at the school, depending on context

Jobbet is the definite form of jobb, meaning the job/work.

In Swedish, the definite article is usually attached to the noun as an ending:

• ett jobb = a job
• jobbet = the job

In expressions like gå till jobbet, Swedish often uses the definite form where English says simply go to work.

So this phrase is idiomatic:

• gå till jobbet = go to work

Also, jobb is an ett-word, so sin jobb would be wrong for more than one reason:

• it should be sitt jobb if reflexive
• but in this expression, Swedish normally says till jobbet

Here så means so, linking the two clauses:

• Hennes skjorta är fortfarande skrynklig
• så hon vill stryka den

So the meaning is:

• Her shirt is still wrinkled, so she wants to iron it.

This så is a coordinating conjunction, similar to English so. Because of that, the word order after it is normal main-clause order:

• så hon vill...

not inversion.

Yes, absolutely.

That version is also correct:

• Innan hon går till jobbet vill hon stryka den.

The main difference is emphasis.

• Hennes skjorta är fortfarande skrynklig, så hon vill stryka den innan hon går till jobbet.
  
  • starts with the reason: the shirt is wrinkled
• Innan hon går till jobbet vill hon stryka den.
  
  • starts with the time frame: before she goes to work

If you move innan hon går till jobbet to the front, Swedish uses inversion in the main clause:

• Innan hon går till jobbet vill hon... not
• Innan hon går till jobbet hon vill...

It is very commonly used for clothes, fabric, paper, and other things that can be creased or wrinkled.

Examples:

• en skrynklig skjorta = a wrinkled shirt
• ett skrynkligt papper = a crumpled/wrinkled piece of paper

For a person’s skin, Swedish more often uses words like rynkig rather than skrynklig.

So in this sentence, skrynklig is exactly the right word for a shirt.