Eftir tónleikana dönsuðum við aðeins á litla dansgólfinu.

Not necessarily. Tónleikar is very often a plural-only noun in Icelandic. Even when English would say a concert, Icelandic commonly says tónleikar.

So:

• tónleikar = a concert / concerts
• tónleikarnir = the concert / the concerts
• eftir tónleikana often means after the concert

This is something learners just have to get used to, because Icelandic and English do not divide this idea the same way.

Because eftir here means after, and in this time meaning it takes the accusative case.

The noun is therefore in the accusative plural definite:

• nominative: tónleikarnir
• accusative: tónleikana

So eftir tónleikana literally means after the concert(s), with tónleikana in the case required by eftir.

No, it is still a statement.

Icelandic main clauses normally follow the verb-second rule. That means the finite verb usually comes in the second slot of the sentence.

Here, the first slot is taken by the time phrase:

• Eftir tónleikana = first slot

So the finite verb comes next:

• dönsuðum = second slot

And then the subject follows:

• við = we

So the structure is:

• Eftir tónleikana | dönsuðum | við | ...

This is normal Icelandic word order, not a question.

Dönsuðum is the 1st person plural past tense of dansa.

So:

• dansa = to dance
• við dönsuðum = we danced

A useful thing to notice is that the stem vowel changes:

• dansa
• dönsuðum

That a → ö change happens because of u-umlaut, triggered by the u in the ending.

So this form means specifically we danced.

Aðeins can mean several close things in English, such as:

• only
• just
• merely
• a little

In this sentence, the most natural sense is something like:

• we only danced a little
• we just danced a bit

It limits the action, not the subject. In other words, it means the dancing was limited in amount or duration.

Because Icelandic uses á for many surfaces or open areas, and a dance floor is thought of that way.

So:

• á dansgólfinu = on the dance floor

This matches English quite well, since English also says on the dance floor.

In Icelandic, á is also common with places like stages, floors, beds, tables, and similar surface-like locations.

Because this sentence describes location, not movement.

With á:

• dative = location, being on something
• accusative = motion onto something

So:

• á litla dansgólfinu = on the small dance floor
• á litla dansgólfið = onto the small dance floor

Here the meaning is that the dancing happened there, so Icelandic uses the dative: dansgólfinu.

Because the adjective is:

• modifying a definite noun
• in the weak declension
• and agreeing with dansgólfinu

The noun dansgólf is neuter singular, and here it is in the dative singular definite. With a definite noun, the adjective normally takes the weak form.

That gives:

• litla dansgólfinu = the small dance floor

Compare:

• lítið dansgólf = a small dance floor
  
  • strong adjective
• litla dansgólfið / litla dansgólfinu = the small dance floor
  
  • weak adjective

So litla is correct because the noun is definite and the adjective must agree with it.

In Icelandic, the is usually attached to the end of the noun as a suffix, instead of being a separate word.

So:

• tónleikana includes the
• dansgólfinu includes the

That is why you do not see a separate word like English the.

Also, when an adjective comes before a definite noun, Icelandic still usually keeps the article on the noun itself:

• litla dansgólfinu = the small dance floor

Here it is definitely the pronoun we.

Icelandic við can be:

• við = we
• við = with (as a preposition)

But in this sentence, it comes where the subject goes:

• dönsuðum við = we danced

If it were the preposition with, it would normally be followed by a noun phrase, for example:

• við vini okkar = with our friends

So in this sentence, við means we.

Yes. Icelandic allows some flexibility, although the emphasis changes.

For example, you could also say:

• Við dönsuðum aðeins á litla dansgólfinu eftir tónleikana.

That is also grammatical. The difference is mainly focus:

• Eftir tónleikana... puts the time frame first, giving it more emphasis.
• Við dönsuðum... starts with the subject, which feels more neutral in some contexts.

Because Icelandic is a verb-second language, the finite verb still has to stay in the second slot of the main clause.

This is the normal Icelandic way to say the small dance floor.

The pattern is:

• weak adjective + definite noun

So:

• litla = small, weak form
• dansgólfinu = the dance floor, dative definite

Together they mean:

• on the small dance floor

This is very common in Icelandic. English uses a separate article, but Icelandic usually marks definiteness directly on the noun and changes the adjective form to match.