Learn Icelandic: Við fáum nokkrar spurningar.

Nokkrar is describing spurningar (questions). Because spurning is a feminine noun, and it is plural here, the word for "several" must also be feminine and plural. It is in the accusative case because it is the direct object receiving the action of the verb fáum (we get).

Is spurningar in the accusative case here? It looks exactly like the nominative!

Yes, it is in the accusative case! For many feminine nouns, the plural form is exactly the same in both the nominative (subject) and accusative (direct object) cases. So spurningar means "questions" whether it is the subject of the sentence or the object being received.

If we wanted to say "We get many questions," how would nokkrar change?

You would use the feminine plural accusative form of margir (many), which is margar. The sentence would simply become: Við fáum margar spurningar.

What is the base form of the verb fáum?

The infinitive is fá (to get or receive). It is a very common but slightly irregular verb. The singular forms look quite different from the plural ones: for example, "I get" is ég fæ, but "we get" is við fáum.