Learn Hardcore Danish: Senere beslutter de sammen, at de vil besøge et museum i weekenden. - Later they decide together that they will visit a museum on the weekend.

When at introduces a subordinate clause, standard comma rules usually put a comma before it:
- De beslutter, at de vil besøge et museum.
  They decide that they will visit a museum.
When at is just the infinitive marker, you do not put a comma before it:
- De beslutter at besøge et museum.
  They decide to visit a museum.

In your sentence, at starts the clause at de vil besøge et museum i weekenden, so it’s a conjunction meaning that, and the comma is normal.

Why is the verb beslutter in the present tense when the sentence starts with Senere (later)?

Danish doesn’t have a special future tense like English. It normally uses:

Present tense + a time expression to talk about the future:
- Senere beslutter de ...
  Literally: Later they decide ...
  Meaning: Later they will decide ... / Later they decide (in the story).
Or a modal verb (vil, skal) plus infinitive:
- Senere vil de beslutte ... – Later they will decide ...

So Senere beslutter de ... is natural Danish. The word senere already tells you it’s in the future relative to some reference point, so the present tense is enough.

Why is it Senere beslutter de ... and not Senere de beslutter ...?

Danish main clauses follow the V2 rule: the finite verb is always in second position in the sentence.

Neutral order: De beslutter senere ...
(de = 1st element, beslutter = 2nd)

If you move something (like Senere) to the front for emphasis or style, the verb must still be the second element:

Senere beslutter de sammen ...
(Senere = 1st element, beslutter = 2nd, de = 3rd)

Senere de beslutter ... would break the V2 rule, so it’s ungrammatical in standard Danish.

Why is it de vil besøge and not de vil besøger?

In Danish, modal verbs (like vil, skal, kan, må) are followed by the infinitive form of the main verb, without -r.

Correct:
- de vil besøge (they will visit / they want to visit)
- de kan besøge
- de skal besøge
Incorrect:
- ✗ de vil besøger
- ✗ de kan besøger

Only one verb in the chain is finite (carries tense and usually ends in -r). Here, vil is the finite verb; besøge stays in infinitive.

Does vil here mean “will” (future) or “want to”? How should I understand de vil besøge et museum?

Vil can mean both “will” (future) and “want to / intend to”, depending on context.

Future / plan:
De vil besøge et museum i weekenden.
= They will visit / are going to visit a museum this weekend.
Desire / intention:
De vil virkelig besøge et museum.
= They really want to visit a museum.

In your sentence, with beslutter de sammen, at de vil besøge ..., the idea is that they decide and thus they will / intend to visit a museum. Both “will visit” and “want to visit” are reasonable readings; English usually chooses “will” in this kind of structure.

Why is it i weekenden and not på weekenden or just i weekend?

A few things are going on here:

Preposition:
For periods of time like weekend, Danish normally uses i to mean “during”:
- i weekenden = during the weekend
- i ferien = during the holiday
- i sommerferien = during the summer holiday
With weekdays, it’s usually på:
- på mandag = on Monday
Definite form:
It’s weekenden, not weekend, because you’re talking about the coming / that specific weekend:
- i weekenden = this/that weekend
- Saying i en weekend = in a/one weekend (some unspecified weekend).

So i weekenden is the idiomatic way to say “at / during the weekend” in this context.

Why is it et museum and not museet?

Danish distinguishes between indefinite and definite nouns:

et museum = a museum (any museum, not specified)
museet = the museum (a specific one already known in the context)

In your sentence, et museum suggests they haven’t specified which museum yet; they just decide to visit a museum.

Also note the gender:

et is the neuter indefinite article.
museum is neuter, so you say et museum.

Why is it de and not dem in de vil besøge et museum?

De and dem are subject vs. object forms:

de = subject form (they)
dem = object form (them)

In de vil besøge et museum, de is the subject (the ones doing the visiting), so you must use de.

Examples:

De besøger dem.
They visit them.
(de = subject, dem = object)
Dem besøger de.
Them, they visit. (emphatic / unusual word order, but still dem as object, de as subject)

Why doesn’t the word order change after at the way it does in German subordinate clauses?

Unlike German, Danish does not move the finite verb to the very end of the subordinate clause.

German:

..., dass sie ein Museum am Wochenende besuchen werden.
(verb at the end)

Danish:

..., at de vil besøge et museum i weekenden.
Subject (de) still comes before the finite verb (vil), and the infinitive (besøge) comes right after.

In Danish subordinate clauses introduced by at, the basic order is:

Subject – (adverb) – finite verb – objects / complements

So at de vil besøge et museum i weekenden keeps a word order that feels much closer to English than to German.

Could we also say De beslutter at besøge et museum i weekenden? What’s the difference from de beslutter, at de vil besøge ...?

Yes, that’s also correct, and very natural:

De beslutter at besøge et museum i weekenden.
= They decide to visit a museum at the weekend.
De beslutter sammen, at de vil besøge et museum i weekenden.
= They decide together that they will visit a museum at the weekend.

Differences:

at besøge (infinitive) = “to visit”
The decision is directly about the action itself.
at de vil besøge (finite clause) = “that they will visit”
Slightly more explicit, focusing on the fact / plan that they will visit.

Both are grammatical; the version with at besøge is usually a bit more compact and common in everyday speech.

Why is sammen placed after beslutter and not at the end of the sentence?

Sammen is an adverb meaning “together”. In your sentence, it describes how they decide, not how they visit:

Senere beslutter de sammen, at de vil besøge et museum i weekenden.
= Later, they decide together that they will visit a museum at the weekend.
(The deciding is done together.)

If you move sammen into the second clause, you change what is “together”:

Senere beslutter de, at de vil besøge et museum sammen i weekenden.
= Later, they decide that they will visit a museum together at the weekend.
(The visiting is done together.)

So its position tells you which action it modifies:
beslutter (decide) in the original sentence, or besøge (visit) if you place it later.