Hvis håndværkeren kommer tidligt, kan hun blive hjemme og åbne døren for ham.

This is because Danish is a V2 language in main clauses: the finite verb usually comes in second position.

Here, the sentence begins with the if-clause:

Hvis håndværkeren kommer tidligt

After that whole clause, the main clause starts. In the main clause, the finite verb must come second, so you get:

kan hun blive hjemme ...

not:

hun kan blive hjemme ...

A useful pattern is:

• Hvis ... , kan hun ...
• Når ... , går jeg ...
• I morgen kommer han ...

So after a fronted element like an adverbial clause, Danish often inverts the normal subject-verb order.

The ending -en is the definite article attached to the noun. Danish often puts the at the end of the word instead of using a separate word.

So:

• en håndværker = a craftsperson / a tradesperson
• håndværkeren = the craftsperson / the tradesperson

This is very common in Danish:

• en dør → døren = the door
• en bil → bilen = the car
• et hus → huset = the house

Here tidligt is being used as an adverb, meaning early.

The base adjective is:

• tidlig = early

When many adjectives are used adverbially in Danish, they take -t:

• hurtig → hurtigt = quickly
• langsom → langsomt = slowly
• tidlig → tidligt = early

So:

• en tidlig morgen = an early morning
  
  • adjective describing a noun
• han kommer tidligt = he comes early
  
  • adverb describing the verb

Because after a modal verb like kan, Danish normally uses the bare infinitive without at.

So:

• kan blive
• kan åbne
• skal gå
• vil komme
• må vente

This is similar to English:

• can stay, not can to stay
• can open, not can to open

So kan hun blive hjemme og åbne døren is completely normal.

Because one modal verb can govern more than one coordinated infinitive.

The structure is:

• kan
  • blive
    • og
      • åbne

This means:

• she can stay home
• and open the door

The verb kan applies to both infinitives. Danish does this very naturally, just like English:

• She can stay home and open the door.

You do not need to repeat kan.

Both can exist, but they are not exactly the same.

• være hjemme = be at home
• blive hjemme = stay at home / remain at home

In this sentence, blive hjemme suggests that she will remain at home instead of leaving, so that she can open the door.

That makes good sense in context:

• If the tradesperson comes early, she can stay home and let him in.

If you said være hjemme, it would sound more like simply be at home, not necessarily stay home on purpose.

Because ham is the object form of the pronoun, while han is the subject form.

• han = he
• ham = him

Here, the craftsperson is the object of the preposition for, so Danish uses ham:

• åbne døren for ham = open the door for him

Compare:

• Han kommer tidligt. = He arrives early.
• Jeg åbner døren for ham. = I open the door for him.

In Danish, åbne døren for nogen is the normal way to say open the door for someone or let someone in.

So:

• åbne døren for ham = literally open the door for him

This is idiomatic and very common. It does not mean she is opening his door; it means she is opening the door for his benefit, usually so he can enter.

Hvis means if in a conditional sense.

In this sentence, it introduces a condition:

• Hvis håndværkeren kommer tidligt ...
• If the tradesperson comes early ...

Danish om can sometimes be translated as if, but it is usually used for whether, not for a condition.

Compare:

• Hvis han kommer tidligt, går vi nu.
  = If he comes early, we’re leaving now.

• Jeg ved ikke, om han kommer tidligt.
  = I don’t know whether he is coming early.

So here hvis is the correct choice.

The comma separates the subordinate clause from the main clause:

• Hvis håndværkeren kommer tidligt, = subordinate clause
• kan hun blive hjemme ... = main clause

In standard Danish, commas are often used around subordinate clauses like this. So the comma helps show the structure clearly.

Not necessarily. The noun håndværker is a common gender noun grammatically, but grammatical gender and real-life sex are not the same thing.

• en håndværker is common gender grammatically
• ham tells you that the person being referred to is male in this context

So the noun itself is not specifically masculine just because it takes en. The pronoun ham is what shows that this particular tradesperson is male.

No, that would be ungrammatical in standard Danish.

Once the sentence starts with the fronted if-clause, the main clause must follow the normal Danish V2 pattern:

• Hvis håndværkeren kommer tidligt, kan hun blive hjemme ...

not:

• Hvis håndværkeren kommer tidligt, hun kan blive hjemme ...

English allows If ..., she can ..., but Danish requires the finite verb before the subject in this situation.

A helpful breakdown is:

1. Hvis håndværkeren kommer tidligt
   = subordinate clause introduced by hvis

2. kan hun blive hjemme og åbne døren for ham
   = main clause

Inside the main clause:

• kan = finite verb
• hun = subject
• blive hjemme = infinitive phrase
• og åbne døren for ham = coordinated infinitive phrase

So the overall pattern is:

If-clause + main clause with inversion

That is a very common Danish structure.