Breakdown of Meine Mutter sagt, Blumenkohl und Zucchini seien im Sommer besonders frisch.
Questions & Answers about Meine Mutter sagt, Blumenkohl und Zucchini seien im Sommer besonders frisch.
Seien is the Konjunktiv I form of sein for they. German often uses Konjunktiv I for indirect speech: it shows that the speaker is reporting someone else’s statement.
So this sentence means something like: My mother says that cauliflower and zucchini are especially fresh in summer, but the German makes it clearer that this is her statement being reported.
Compare:
Direct statement:
Blumenkohl und Zucchini sind im Sommer besonders frisch.
Reported speech:
Meine Mutter sagt, Blumenkohl und Zucchini seien im Sommer besonders frisch.
No. It is not required in everyday German.
You could also say:
Meine Mutter sagt, Blumenkohl und Zucchini sind im Sommer besonders frisch.
or
Meine Mutter sagt, dass Blumenkohl und Zucchini im Sommer besonders frisch sind.
Using seien sounds more like formal reporting, written German, journalism, or careful style. In normal conversation, many speakers would simply use sind.