Jeg regner med, at min søster kommer efter arbejde, men hun har ikke skrevet endnu.

Yes. On its own, regne often means to count or to calculate. But the expression regne med is an idiom, and it commonly means:

• to expect
• to assume
• to count on

So Jeg regner med, at ... means something like I expect that ... or I’m assuming that ...

It does not sound strange to a Danish speaker, even though the literal parts might look odd to an English learner.

At is the conjunction that.

So:

• Jeg regner med, at min søster kommer ...
• I expect that my sister is coming ...

In Danish, at is often used to introduce a subordinate clause after verbs of thinking, saying, expecting, knowing, and so on.

In everyday speech, Danes may sometimes omit at, especially in informal language, but with a sentence like this, using at is completely normal and standard.

Because at introduces a subordinate clause, and subordinate clauses in Danish usually follow normal subject-verb order:

• min søster kommer

That is:

• subject: min søster
• verb: kommer

In main clauses, Danish often puts the verb in second position, which can create inversion. But after at, you normally do not invert the subject and verb.

So:

• main clause: Hun kommer efter arbejde
• subordinate clause: ... at min søster kommer efter arbejde

Danish often uses the present tense to talk about planned or expected future events, just like English sometimes does.

So:

• min søster kommer efter arbejde
  can mean
• my sister is coming after work

This is very natural in Danish.

If you say vil komme, that can sometimes sound more like:

• will come
• wants to come
• or a more explicit future meaning, depending on context

In this sentence, kommer sounds simpler and more idiomatic.

Efter arbejde means after work.

Danish often uses certain nouns without an article in common time/place expressions, especially with everyday routines. Compare:

• på arbejde = at work
• fra arbejde = from work
• efter arbejde = after work

So Danish works a lot like English here: English also says after work, not after the work, in this kind of general daily-life meaning.

If you said efter arbejdet, that would more likely mean after the work or after the task/job, referring to something more specific.

Har skrevet is the present perfect tense.

It is formed with:

• har = have/has
• past participle: skrevet = written

So hun har ikke skrevet endnu means:

• she has not written yet

This tense is used because the speaker is talking about something that has not happened up to now.

It fits the idea of yet very well:

• She hasn’t written yet
• Hun har ikke skrevet endnu

In this sentence, skrevet does not necessarily mean writing a formal letter. In modern Danish, skrive can often mean:

• write
• send a message
• text
• contact in writing

So hun har ikke skrevet endnu naturally means something like:

• she hasn’t written yet
• she hasn’t messaged yet
• she hasn’t texted yet

The object is left unstated because it is understood from context.

In the perfect tense, the negation ikke usually comes after the auxiliary verb and before the past participle.

So:

• hun har ikke skrevet endnu

Breakdown:

• hun = she
• har = has
• ikke = not
• skrevet = written
• endnu = yet

This is the normal position:

• har ikke skrevet
• er ikke kommet
• kan ikke forstå

So if you are building Danish sentences, a good pattern is:

subject + auxiliary/modal + ikke + main verb/participle

They do different jobs:

• ikke = not
• endnu = yet/still, depending on context

In hun har ikke skrevet endnu, endnu means yet.

So:

• hun har ikke skrevet endnu = she hasn’t written yet

Without endnu, the sentence would simply mean:

• she hasn’t written

That is grammatical, but endnu adds the idea that the speaker still expects it may happen later.

Because Danish comma rules usually place a comma before a subordinate clause and before coordinating conjunctions like men.

So here you get:

• Jeg regner med, at min søster kommer efter arbejde, men hun har ikke skrevet endnu.

The commas separate:

1. the main clause from the at-clause
2. the first part of the sentence from the contrasting clause introduced by men = but

Danish comma usage is often a bit more visible than in English, so learners commonly notice this.

Yes, you could, but the tone is a little different.

• Jeg regner med, at ... = I expect / I’m assuming / I’m counting on ...
• Jeg forventer, at ... = I expect ...

Forventer can sometimes sound a little stronger or more formal, depending on context.
Regner med often feels more everyday and conversational.

So in this sentence, Jeg regner med, at ... is a very natural choice.

Yes, min søster means my sister.

Søster is a common gender noun in Danish, so the possessive is min:

• min søster = my sister
• min ven = my friend
• min bil = my car

With a neuter noun, you would use mit instead:

• mit arbejde = my work
• mit hus = my house

And for plural, you use mine:

• mine søstre = my sisters

So min is correct because søster is a common gender singular noun.