Learn German: Die Mutter macht sich große Sorgen.

In German, you don't say you "are worried." Instead, you use the reflexive phrase sich Sorgen machen, which literally translates to "to make worries for oneself."

Is the reflexive pronoun sich in the accusative or dative case here?

It is in the dative case. The direct object of the sentence is große Sorgen (the thing being made), which takes the accusative case. Because the accusative spot is taken, the reflexive pronoun falls into the dative case. If you wanted to say "I am worried," you would use the dative pronoun for yourself: Ich mache mir Sorgen.

The English translation says "very worried," but the German uses große. Why is that?

Because the German phrase uses the noun Sorgen (worries) rather than an adjective, you cannot use an adverb like sehr (very) to intensify it. Instead, you must use an adjective to describe the noun, which is why a German speaker makes "big worries" (große Sorgen).

Is Sorgen always plural in this phrase?

Yes, the set phrase is almost always plural: sich Sorgen machen. The singular noun die Sorge exists, but when talking about worrying in general, Germans default to the plural.