Vi besøger en kvinde, hvis søster cykler til universitetet hver dag på samme cykelsti.

Yes. Danish does not have a separate present progressive form like English are visiting. The simple present besøger can mean either visit or are visiting, depending on context.

So Vi besøger en kvinde can mean:

• We visit a woman
• We are visiting a woman

The same applies to cykler later in the sentence.

En kvinde is the indefinite form, meaning a woman. You use the indefinite form when introducing someone or something for the first time.

• en kvinde = a woman
• kvinden = the woman

So this sentence is talking about a woman not already identified in the sentence.

The part hvis søster cykler til universitetet hver dag på samme cykelsti is a relative clause describing en kvinde.

In Danish, many writers put a comma before this kind of clause:

• en kvinde, hvis søster...

In modern Danish, this start comma is optional, so you may also see:

• en kvinde hvis søster...

Both are possible, though the comma is very common and often helps readability.

Because hvis shows possession. Here it means whose.

• som = who / which / that
• hvis = whose

So:

• en kvinde, hvis søster... = a woman whose sister...

You cannot use som here, because the sentence needs a possessive link between kvinde and søster.

No. Hvis can also mean if in some contexts, especially in formal or written Danish.

But in this sentence, it clearly means whose, because it is followed by a noun:

• hvis søster = whose sister

That structure makes the possessive meaning obvious.

After a possessive word such as hvis, the noun normally stays in its basic indefinite form.

So:

• hvis søster = whose sister
• not hvis søsteren

This is similar to English:

• whose sister
• not whose the sister

Other examples:

• min bil = my car
• hendes bror = her brother

It is a verb here.

• at cykle = to cycle / to ride a bike
• cykler = present tense, cycles / rides a bike

So søster cykler til universitetet means the sister goes there by bicycle.

As a noun, cykel means bicycle, but here the ending and position show that cykler is the verb.

Because this relative clause has normal subject-verb order.

• hvis søster = subject
• cykler = verb

So the order is:

• subject + verb + other information

Danish only puts the verb before the subject in certain main-clause patterns, often when something else comes first. Inside this relative clause, regular order is used:

• hvis søster cykler til universitetet...

Because til shows movement to a place.

• cykler til universitetet = cycles to the university
• er på universitetet = is at the university

So:

• til answers where to?
• på answers where?

If the idea is travel toward the university, til is the natural choice.

Because universitet is a neuter noun:

• et universitet = a university
• universitetet = the university

The ending -et is the definite singular ending for many neuter nouns.

In Danish, it is very normal to use the definite form after til when talking about going to a particular place:

• til skolen
• til stationen
• til universitetet

Even where English might sometimes say to university, Danish often uses the definite form.

Hver dag means every day and works as a time expression.

In this sentence it comes after the destination:

• cykler til universitetet hver dag

That is a very natural Danish order. After the verb, Danish often places information in a fairly flexible sequence, but this version sounds smooth and ordinary:

• verb
• destination
• time
• extra location/detail

So til universitetet hver dag på samme cykelsti is a natural way to build the sentence.

Both can be possible, but they are not exactly the same in feel.

• samme cykelsti = the same bike path
• den samme cykelsti = also the same bike path, often with a bit more emphasis

In this sentence, på samme cykelsti is natural and compact. After samme, the noun usually stays in its basic form:

• samme bog
• samme vej
• samme cykelsti

So you do not say samme cykelstien.

En cykelsti means a cycle path, bike path, or sometimes bike lane, depending on context.

It is made from:

• cykel = bicycle
• sti = path

So på samme cykelsti means the sister uses the same bicycle path every day.

For this exact structure, hvis is the natural and correct choice, because the relationship is possessive: the woman has a sister.

You could only use som if you rewrote the sentence completely, for example:

• Vi besøger en kvinde, og hendes søster cykler til universitetet hver dag på samme cykelsti.

But in the original sentence, hvis is the right relative word because it neatly means whose.