Min søster siger, at sådan en mørk sky ofte betyder, at der snart kommer en byge.

In Danish, a possessive like min, mit, or mine normally replaces the article and the definite ending.

So you say:

• min søster = my sister
• søsteren = the sister

That means min søsteren is not standard Danish.

Also, min is used because søster is a singular common-gender noun. Compare:

• min søster
• mit hus
• mine søstre

Sådan en means something like such a, that kind of, or a ... like that, depending on context.

So sådan en mørk sky means:

• such a dark cloud
• a dark cloud like that
• that kind of dark cloud

It points to a type of thing, not just any cloud in general.

Because sky is a common-gender noun in Danish, so it takes en, not et.

With a common-gender singular noun in the indefinite form, the adjective usually has no extra ending:

• en mørk sky

If the noun were neuter, you would use et and the adjective would usually take -t:

• et mørkt rum

So:

• en sky
• en mørk sky

are the correct forms.

Both at words here mean that and introduce subordinate clauses.

1. Min søster siger, at ...
   = My sister says that ...

2. ... betyder, at ...
   = ... means that ...

So the sentence has one clause inside another, and each new subordinate clause is introduced by at.

This is different from the other common use of at, where it marks an infinitive, as in:

• at komme = to come

In your sentence, both at words are conjunctions meaning that.

This is a very common Danish word-order point.

In a main clause, Danish normally puts the finite verb in second position:

• Sådan en mørk sky betyder ofte ...

But after at, you are in a subordinate clause, and the word order changes. In subordinate clauses, the verb does not have to stay in second position, and adverbs like ofte commonly come before the finite verb:

• at sådan en mørk sky ofte betyder ...

So the placement of ofte is a clue that this is a subordinate clause.

Here der is not really the location word there. It is an expletive or dummy subject.

In Danish, der is often used when something new or indefinite is being introduced:

• Der kommer en bil
• Der sidder en mand udenfor
• Der snart kommer en byge

So at der snart kommer en byge means something like:

• that a shower is coming soon
• that there will soon be a shower

The real thing being introduced is en byge, but Danish often uses der in this kind of structure.

Because Danish often uses the present tense for future meaning when the context already makes the time clear.

Here, snart tells you it is about the near future:

• der snart kommer en byge

So Danish does not need a separate future form here. This is very natural.

English does something similar in some cases:

• I’m leaving tomorrow

Danish can also use vil for future, but in a sentence like this, the simple present is the most natural choice.

En byge means a shower: a short period of rain, snow, or similar weather.

So it is not just rain in general. It suggests something brief and sudden.

Compare:

• regn = rain in general
• en byge = a shower
• en regnbyge = a rain shower

In your sentence, en byge fits well because a dark cloud can be a sign that a short burst of rain is coming.

The commas mark subordinate clauses.

Your sentence has:

• Min søster siger, at ...
• ... betyder, at ...

In Danish, many learners first see sentences written with commas before subordinate clauses like these.

However, modern Danish also allows a system without the so-called start comma, so you may also see:

• Min søster siger at sådan en mørk sky ofte betyder at der snart kommer en byge.

So if you notice commas before at, that is normal. If you do not see them, that can also be correct, depending on the comma style being used.

Yes, but it sounds a bit more formal or written.

The version in your sentence:

• sådan en mørk sky

is very natural in everyday Danish.

The version:

• en sådan mørk sky

is understandable and grammatical, but it is less common in ordinary speech.

So for spoken, natural Danish, sådan en + noun is usually the better pattern.